Numerical simulation of air resistance of French drains beneath geomembrane in field vacuuming tests
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摘要: 膜下盲沟是水库土工膜防渗方案的重要工程措施，对膜下气体排出具有决定性作用。基于流量变化等效原则，提出了渗透系数与路径长度的平方成比例的变换关系。据此推断出水库面积巨大，排气路径太长，是盲沟气阻引发膜下气胀的主要原因。运用非饱和土固结简化计算方法模拟了抽气条件下膜下气压分布状态；对比现场试验实测值，验证了计算方法和参数的合理性。计算结果表明：无论有无盲沟，膜下沿水平向分为气压急变区和稳定区，气压急变区为抽气点沿水平向2.5 m范围，区内气压显著变化，反映了盲沟气阻的存在性；膜下气压梯度分布规律反映盲沟气阻的变化；影响盲沟气阻的主要因素是材料进气值和饱和度，进气值减小、饱和度降低均有利于减小盲沟气阻。研究成果可为合理评价库盘土工膜防渗方案设计提供科学理论依据。Abstract: The French drains beneath the geomembrane are an important engineering measurement for the geomembrane as anti-seepage structures of reservoirs, and have a decisive effect on the air exhaust beneath the geomembrane. The conversion relationship between the permeability coefficient and the square of path length is proposed on the basis of the principle of equivalent flow variation. It is deduced that the important reasons for the bulge of the geomembrane are the huge reservoir area and the long drain path because of the air resistance of French drains. The simplified method for consolidation of unsaturated soils is used to calculate and simulate the air pressure distribution beneath the geomembrane under the condition of vacuuming. The comparison between the measured and calculated values in the field tests has verified the rationality of the proposed method and parameters. The results reveal that a pressure changing zone and a stable zone exist along the horizontal direction whether there is a French drain or not. The pore-air pressure changes significantly in the zone of a range of 2.5 m along the horizontal direction from the vacuuming spot, which indicates the existence of the air resistance of French drain. The distribution of pressure gradient beneath the geomembrane reflects the change of the air resistance of French drain. The main influencing factors for the air resistance of French drain are the air intake value and the degree of saturation of materials. Reducing the air intake value and lowering the degree of saturation are beneficial to reducing the air resistance of French drain. The research results may provide a scientific theoretical basis for the evaluation of the design of anti-seepage scheme of the geomembrane.
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0. 引言
随着中国交通行业的不断发展,中国桥梁建设水平得到大幅提升,对桥梁跨越能力的要求也不断增长,悬索桥作为所有桥型中跨越能力最大的桥型,越来越成为跨越大江、大河的主要解决方案。但是随着悬索桥跨度的不断增加,锚碇规模急剧扩大,造成锚碇建设成本过高。因此研究锚碇沉井基础的受力变形特性对于悬索桥的锚碇优化设计显得尤为重要。
Alampalli[1]在1994年研究了沉井在承受竖向和水平向荷载时的结构响应；李永盛[2]和李家平等[3]分别在1995年和2005年通过模型试验探讨了沉井基础的变形机制和破坏失稳形式；穆保岗等[4]在2017年通过模型试验研究了水平荷载长期作用下沉井变位的特性；Liu等[5]在2019年通过模型试验结合数值模拟分析研究了重力式锚碇的稳定性。
本文首先进行了在分级水平荷载下的沉井在砂箱中的模型试验,然后基于PLAXIS 3D软件建立了有限元模型,并分析了沉井的位移及沉井前侧和沉井底部的土压力,研究了水平荷载条件下沉井的受力变形规律。
1. 依托工程及模型试验
本文依托南京仙新路大桥北锚碇沉井工程,沉井长度为70 m,宽度为50 m,高度为49.5 m。该工程地基土以粉砂和中砂为主。
本试验采用的模型槽平面尺寸为4.0 m×2.0 m,高1.0 m。地基土采用中砂,其相对密度为2.68,最大孔隙比0.881,最小孔隙比0.463,不均匀系数3.89,曲率系数0.92。模型试验分层填筑地基土,控制每层填土的厚度为0.1 m,最终得到地基土的干密度为1.55 g/cm3,含水率0.63%,相对密实度为59.61%,内摩擦角为34.5°（快剪）。
沉井模型平面尺寸为0.7 m×0.5 m,高0.495 m,由厚度为22 mm的钢板焊接而成,试验过程将沉井看成刚体,不考虑沉井自身的变形,为模拟沉井与土体相互作用的界面,通过在沉井表面黏2～3 mm的砂粒实现[6],如图1所示。
模型试验中设计荷载为62kg,本文中水平荷载分级施加,每级荷载为设计荷载的～0.5倍,试验过程中每级荷载施加持续15 min直至土体破坏（土体破坏表现为沉井盖板处的位移急剧增大）,沉井加载示意图如图2所示。
2. 有限元分析
本研究建立的有限元模型完全基于模型试验,土体及沉井的单元形状均为四面体十节点实体单元,数值模型的网格如图3所示。
砂土的本构模型采用土体硬化（HS）模型,土层参数[7]取值见表1。
表 1 土层参数Table 1. Soil parameters土层 /(kN·m-3) e /MPa /MPa /MPa /MPa /(°) /(°) m 砂土 15.6 0.723 10.2 10.2 10.2 30.6 0 34.5 0 0.5 注： 为砂土的重度； 为砂土的孔隙比； 为砂土的压缩模量； 为砂土的主固结加载切线刚度； 为砂土的标准三轴排水试验割线刚度； 为砂土的卸载重加载刚度； 为砂土的有效黏聚力； 为砂土的有效摩擦角； 为砂土的膨胀角； 为砂土的刚度应力水平相关幂值。 3. 试验结果与有限元结果对比
3.1 沉井顶部位移
在沉井盖板顶部设置3个位移测量点A、B、C。在位移测量点上放置位移靶标,采用TH-ISM-ST机器视觉测量仪对靶标位移进行测量,分辨率为0.01 mm,靶标布置如图4。
模型试验和数值模拟的位移对比如图5所示,由图易知,模型试验和数值模拟的靶标位移较为一致,本文中取水平位移随设计荷载增加而不断增加的线弹性阶段为水平承载力极限值[4],即安全系数取值为4。
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图 5 模试验和数值模拟的位移对比Figure 5. Comparison of displacements between model tests and numerical simulations3.2 沉井前侧壁土压力随施加荷载变化
在沉井前侧设置8个土压力盒,布置如图6所示,由于土压力盒对称分布,且沉井左右侧完全对称,因此取沉井左右两侧土压力盒平均值作为最终结果,结果如图7所示,其中模型试验中3号及3＇号土压力盒数据较差,本文中已舍弃,余下的沉井前侧土压力盒数据和数值模拟结果较吻合。
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图 7 模试验和数值模拟的沉井前侧土压力对比Figure 7. Comparison of soil pressures on front side of caisson between model tests and numerical simulations3.3 沉井前侧壁土压力随施加荷载变化
在沉井底部设置12个土压力盒,布置如图8所示,同理,取沉井左右两侧土压力盒平均值作为最终结果,结果如图9所示,其中8号及8＇号土压力盒数据较差,本文中已舍弃,余下的沉井底部土压力盒数据和数值模拟结果对比,发现当施加荷载/设计荷载的值小于等于4时较一致,当其值大于4之后,二者的结果相差较大。
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图 9 模型试验和数值模拟的沉井前侧土压力对比Figure 9. Comparison of soil pressures on bottom of the caisson between model tests and numerical simulations4. 结论
本文在已有的研究基础上,通过开展模型试验和数值模拟计算,得到水平荷载下沉井的受力变位特性,主要得出以下结论：
（1）对锚碇沉井基础在砂土中的受力变位特性进行了试验研究和有限元分析,结果显示,水平荷载下锚碇沉井基础在砂土中的破坏模式为倾覆破坏,且安全系数远大于2,说明现阶段规范[8]中锚碇设计较为保守,有进一步的优化空间。
（2）通过PLAXIS 3D软件建立了锚碇沉井基础的有限元模型,采用应变硬化的本构模型,结果表明模型试验的结果和有限元模型计算的结果较为一致,说明数值建模过程中的土体本构模型及参数取值可靠,表明PLAXIS 3D软件能够较好的模拟锚碇沉井在砂土中的受力变形行为。
上述模型试验和有限元分析,只是针对水平荷载条件下锚碇沉井基础在砂土中的受力特性开展的研究,只考虑了单层干砂的地基土层,尚需更近一步探索。
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图 3 水库膜下排气排水系统布置图
Figure 3. Layout of French drain system beneath geomembrane of reservoir
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图 6 抽气范围内膜下气压计算结果
Figure 6. Calculated results of pore-air pressure beneath geomembrane by field vacuuming tests
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图 7 膜下抽气点附近的气压计算结果
Figure 7. Pore-air pressures beneath geomembrane near vacuuming spot
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图 8 不同深度处气压与距离的关系
Figure 8. Relationship between air pressure and distance at different depths
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图 9 不同位置处气压与深度的关系
Figure 9. Relationship between air pressure and depth at different distances
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图 10 不同深度处气压梯度与距离关系
Figure 10. Relationship between air pressure gradient and distance at different depths
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图 11 不同距离处气压梯度与深度关系
Figure 11. Relationship between air pressure gradient and depth at different distances
表 1 非线性E-μ模型计算参数
Table 1 Parameters of E-μ model for air field beneath geomembrane
土料 γ/(kN·m-3) φ/(°) c/kPa Rf K n G F D Kur Kws/(m·s-1) Kd/(m·s-1) e Sr0/% Srl/% λ usb/kPa 角砾土 22.4 30 10 0.93 400 0.6 0.3 0.15 1.5 800 3×10-4 3.22×10-3 0.53 0.90 0.11 4.1 3.1 盲沟 18.0 22 0 0.95 300 0.6 0.3 0.20 1.9 800 0.2 0.2 0.53 0.85 0.11 4.1 0.5 防渗膜 0.036 22 100 0.93 300 0.6 0.3 0.17 1.0 650 5.0×10-11 5.0×10-11 0.064 — — — — 
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表 2 膜下气压的现场试验值
Table 2 Pore air pressures beneath geomembranes by in-situ tests
项目 最低值/kPa 最高值/kPa 平均值/kPa 数据量/个 均方差/kPa TP01 -0.90 -0.46 -0.68 11 0.13 TP02 -0.97 -0.56 -0.76 11 0.13 TP03 -0.80 -0.47 -0.64 11 0.11 TP04 -0.46 -0.23 -0.34 11 0.08 GP01 -2.67 -2.30 -2.49 11 0.12 GP02 -1.02 -0.48 -0.77 11 0.18 GP03 -1.10 -0.43 -0.85 11 0.22 注：TP是埋设于土体中渗压计；GP是埋设于盲沟内的渗压计。GP01是盲沟与真空泵连接部位的渗压计，即为试验场地的抽气点。
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