Experimental study on freezing deformation characteristics of unsaturated expansive soils considering cyclic freeze-thaw and initial anisotropy
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摘要: 地处季冻区的膨胀土胀缩变形显著，由此诱发的工程隐患与灾害尤为严重。为探究循环冻融历史与初始各向异性影响下非饱和膨胀土的冻结变形特征，开展了压实膨胀土的循环冻融和体变量测试验。试验结果表明：①相较于融化状态，膨胀土在冻结状态下的体积应变受干密度与含水率影响更显著，含水率越高、干密度越大，试样融化和冻结状态下的体积应变差异越大。②膨胀土试样冻结体变随初始饱和度增加呈先减小后增大的变化趋势，且表现为低饱和度时“冻缩”，高饱和度时“冻胀”。③试样的冻结体积应变与含水率呈二次函数关系，存在一个“临界含水率”特征值，使得试样的体积收缩率最大。④循环冻融作用下，低含水率试样的冻结体积应变较高含水率时更易稳定；轴向应变随冻结次数的累积效应较径向应变更为显著。⑤压实作用诱导膨胀土试样冻结变形呈各向异性，且含水率越高，冻结变形各向异性越显著。研究结果可为季冻区膨胀土地段工程的变形控制和灾害防治提供参考。Abstract: The swelling and shrinkage deformation of the expansive soils in seasonally frozen regions is significant, which seriously induces engineering hazards and disasters. To investigate the freezing-induced deformation characteristics of the unsaturated expansive soils under the influences of cyclic freeze-thaw and initial anisotropy, a series of cyclic freeze-thaw tests and volumetric variation measurement tests on the compacted expansive soils are carried out. The test results show that: (1) Compared with the melting state, the volumetric strain of the expansive soils in freezing state is more significantly affected by the dry density and water content. The higher the water content and dry density, the greater the difference of frozen and melted volumetric strains. (2) With the increase of the initial saturation, the frozen volumetric strain of the expansive soil samples first decreases and then increases, indicating freezing shrinkage at low saturation and freezing swelling at high saturation. (3) There is a good quadratic relationship between the frozen volumetric strain and the water content, and there exists a characteristic value of "critical water content", at which the maximum volumetric shrinkage occurs. (4) Under the cyclic freeze-thaw action, the frozen volumetric strain of the samples with low water content is more stable than that with the higher water content. The cumulative effects of the axial strain with freezing times are more significant than those of the radial strain. (5) The frozen deformation has compaction-induced anisotropy, which is more significant at higher water contents. The research results can provide reference for the deformation control and disaster prevention of the expansive soils in seasonally frozen regions.
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Keywords:
- expansive soil /
- freeze-thaw cycle /
- freezing deformation /
- anisotropy /
- deformation mechanism
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0. 引言
足尺试验是了解盾构隧道结构力学行为的有效方法。许多学者开展了足尺管片接头试验来研究纵缝接头的变形特征和力学特性[1-3]。隧道管片纵缝接头在持续加载作用下的力学性能是以往研究的重点，而很少研究在应用修复措施治理隧道大变形时纵向接缝的变形和力学特性、可恢复性以及恢复效率[4]。
本文通过开展盾构隧道拱顶双缝接头和拱腰单缝接头的原型足尺试验，旨在探究两类接头在隧道上方堆载作用下的变形发展规律，分析盾构隧道管片在恢复过程中各性态特征的演化规律，评价不同既有变形条件下隧道管片不同部位接头变形的恢复效果。
1. 接头试件设计
本文针对上海地铁隧道运用的管片衬砌环中的纵缝接头进行一系列室内结构原型试验，隧道衬砌环和纵缝接头构造形式如图 1所示。试验试件包括两类接头，分别为位于隧道管片环拱顶位置受正弯矩作用的纵缝接头(即封顶块和邻接块连接处接头，以下称为拱顶接头)和位于隧道管片环拱腰位置受负弯矩作用的纵缝接头(即邻接块和标准块连接处接头，以下称为拱腰接头)，如图 2所示。弯矩以衬砌环内侧受拉为正，轴力以受压为正。
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图 1 上海地铁盾构隧道管片衬砌结构Figure 1. Structure of segment linings of shield tunnel in Shanghai Metro![]()
图 2 试验现场照片：(a)拱顶接头试件；(b)拱腰接头试件；(c)位移传感器布置；(d)隧道衬砌环横截面图Figure 2. Photos of test set-up: (a) Specimen of longitudinal joint at tunnel crown, (b) Specimen of longitudinal joint at tunnel waist, (c) Arrangement of displacement sensors, (d) Cross-sectional view of tunnel lining ring值得注意的是，隧道拱腰和拱脚纵缝是径向平直面，而拱顶纵缝是与径向斜交的平直面，拱顶纵缝接头是楔形结构，见图 1(a)。然而，以往研究中采用的是简化的如拱腰一样的直缝结构，不能准确描述拱顶处实际的斜接缝构造的力学行为。本文采用隧道拱顶双接头形式进行试验研究。
2. 管片接头内力计算
采用考虑接头非线性刚度的盾构隧道衬砌分析模型[5]计算接头内力(弯矩、轴力和剪力)。如图 3所示，隧道埋深15 m，周围土体为典型的上海软土，饱和重度(γ)为18 kN/m3，静止侧压力系数(K0)为0.65，地层抗力系数(KS)为6000 kN/m3。该模型首先通过对隧道结构施加竖向压力来模拟地面超载对隧道变形的影响。然后，通过移除竖向压力来模拟卸载。最后，通过对隧道结构施加侧向压力模拟注浆对隧道变形的恢复作用。根据接头内力计算结果可以确定足尺试验中对应不同工况的加载路径。
试验中，通过水平和垂直液压千斤顶向试件施加水平载荷和垂直载荷，以模拟接头内力(即弯矩、轴力和剪力)，见图 2中(a)和(b)。图 4和图 5分别为试验中拱顶接头和拱腰接头的受力分析图。根据力矩平衡方程，拱顶接头试件和拱腰接头试件的外部载荷和内力之间的关系可由式(1)和式(2)分别推导得到。
{M=G⋅L2+P⋅(L2−L1)−N′⋅hN=N′⋅cosθ+12G⋅sinθQ=N′⋅sinθ+12G⋅cosθ， (1) {M=P⋅L2−G⋅(L1−L2−L3)−N′⋅hN=N′。 (2) 式中G为管片重力；M，N，Q分别为接头处弯矩、轴力和剪力；N′和P分别为由水平液压千斤顶和竖向液压千斤顶施加的水平向荷载和垂向载荷，通过POP-M工控PC电液伺服多通道控制器实现试验进程的自动控制。
3. 试验加载方案
针对拱顶接头和拱腰接头共开展了6组试验，工况Ⅰ~Ⅲ和工况IV~VI分别研究拱顶接头和拱腰接头超载变形后通过卸载和注浆的变形恢复过程，具体试验过程见表 1。试验在同济大学岩土及地下工程教育部重点实验室进行，采用TJ-GPJ2000盾构管片接头试验加载系统。试验过程中接缝张开量由线性位移传感器(LVDT)测得，如图 2中(c)所示。
表 1 试验工况Table 1. Test design工况编号 接头类型 试验内容 加载过程 试验控制变量 变量值 正常荷载
水平工况Ⅰ 拱顶接头 变形恢复过程 加载至正常荷载水平→施加超载→卸载至正常荷载水平→注浆过程模拟 超载程度/接头内力；
弯矩M，
轴力S，
剪力QM=178 kN/m，
N=593 kN，
Q=88 kN拱顶接头：
M=118 kN/m，
N=590 kN，
Q=87 kN
拱腰接头：
M=98 kN/m，
N=816 kN工况Ⅱ M=278 kN/m，
N=927 kN，
Q=134 kN工况Ⅲ M=378 kN/m，
N=1260 kN，
Q=181 kN工况Ⅳ 拱腰接对 M=155 kN/m，
N=968 kN工况Ⅴ M=171 kN/m，
N=1068 kN，工况Ⅵ M=188 kN/m，
N=1175 kN4. 试验结果与分析
4.1 拱顶接头
图 6对比显示了受正弯矩作用的隧道拱顶接头在工况Ⅰ~Ⅲ中接缝张开增量的变化。在超载过程中，接头张开量随着荷载的增加而增大。当3工况试件达到最大荷载时，接头变形也达到峰值。在卸载过程中，试验结果表明卸载能在一定程度上恢复接头变形，但不能完全恢复。接头变形卸载恢复百分比，即卸载减少的接缝张开增量与卸载前接缝张开增量的比值，分别为68%，56%，43%。这表明超载越小即变形程度越小，接头变形的可恢复性越好。
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图 6 工况Ⅰ~Ⅲ中拱顶接头在超载、卸载和土体注浆过程中的荷载–变形关系曲线Figure 6. Load-deformation curves of longitudinal joints at tunnel crown during overloading, unloading and soil grouting conditions for test cases Ⅰ~Ⅲ针对土体注浆对拱顶接头变形恢复的试验模拟，试验结果表明，其荷载–变形曲线的斜率比卸载过程小得多。减小相同的弯矩，土体注浆可使接头变形得到更有效的恢复，这是因为土体注浆引起的拱顶弯矩减小和轴力增大导致偏心距减小。为了在卸载后将接头变形完全恢复到正常载荷状态下的水平，工况Ⅰ~Ⅲ需要通过模拟土体注浆分别减小弯矩值为20，25，40 kN·m，如图 6所示。
4.2 拱腰接头
图 7对比显示了受负弯矩作用的隧道拱腰接头在工况Ⅳ~Ⅵ中接缝张开增量的变化。在超载阶段，相同载荷水平下，3工况的接缝张开增量几乎相同。荷载–变形曲线斜率的减小表明拱腰接头试件的抗弯刚度随着超载水平的增加而降低。在此基础上，研究了卸载和注浆作用下的变形恢复效果。接头变形卸载恢复百分比分别为65%，42%，36%。显然，与拱顶接头呈现的特性一样，变形程度越小卸载恢复效果百分比越大。
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图 7 工况Ⅳ~Ⅵ中拱腰接头在超载、卸载和土体注浆过程中的荷载–变形关系曲线Figure 7. Load-deformation curves of longitudinal joints at tunnel waist during overloading, unloading and soil grouting conditions for test cases Ⅳ~Ⅵ在试验模拟土体注浆阶段，荷载–变形曲线的斜率明显小于卸载阶段。在隧道两侧注浆产生的侧向挤压力的作用下，接头偏心距减小。因此，通过减少相同的弯矩，土体注浆比卸载获得更有效的恢复。此外，为了将变形恢复到正常荷载状态的水平，即将接缝张开增量减小到零，试验结果显示工况Ⅳ~Ⅵ分别需要减少弯矩为16，42，48 kN·m。
从两类接头的试验结果可知：超载作用下接头张开变形呈现出非线性发展规律，总体上，两类接头的抗弯刚度随着接头已有张开变形的增大而降低；超载引起的变形可以通过卸载得到部分恢复，既有变形越小，恢复效果越好，但不能完全恢复到超载之前状态；注浆作用下，拱顶接头的变形恢复效果较拱腰接头更为显著，这是由于注浆产生的横向挤压作用在减小拱顶接头弯矩的同时亦增大了其轴力，即有效降低了拱顶接头处的偏心距。
5. 结论
本文介绍了上海地铁隧道管片衬砌纵缝接头的一系列室内足尺试验结果，初步探究了卸载和土体注浆对超载引起接头变形的可恢复性，得出以下结论：
(1) 在地面超载作用下，衬砌环发生较大的横向变形，拱顶接头向隧道管片内侧张开，拱腰接头向隧道管片外侧张开，导致渗漏水等隧道病害发生的概率增大。
(2) 超载引起的变形能够通过卸载恢复部分变形，既有变形越小，恢复效率越高。当减少相同的弯矩时，土体注浆比卸载能实现更有效的恢复。
(3) 由于隧道衬砌环中的所有纵缝接头钢螺栓均靠近管片内侧，拱腰接头抗弯能力较拱顶接头差，转动刚度较小，变形较大，变形恢复效果较差。此外，注浆作用下，拱顶接头的变形恢复效果较拱腰接头更为显著，其原因是注浆有效降低了拱顶接头处的偏心距。因此，建议加强拱腰接头处结构设计，增强其抗弯强度，从而提升隧道衬砌的整体安全性能。
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图 4 不同含水率下试样体积应变与干密度关系
Figure 4. Relationship between volumetric strain and dry density of samples with different water contents
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图 5 不同干密度下试样体积应变与含水率关系
Figure 5. Relationship between volumetric strain and water content of samples with different dry densities
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图 6 试样冻结后体积应变与饱和度关系
Figure 6. Relationship between volumetric strain and saturation of frozen samples
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图 8 不同冻结次数下体积应变随含水率变化规律
Figure 8. Variation of volumetric strain with water content under different freezing times
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图 9 相同负温下冻结后空隙体积变形示意图
Figure 9. Diagram of volume deformation of void after freezing under same negative temperature
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图 10 临界含水率、最大收缩应变与干密度的关系
Figure 10. Relationship among critical water content, peak shrinkage strain and dry density of samples
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图 11 临界含水率、最大收缩应变随冻结次数变化规律
Figure 11. Variation of critical water content, peak shrinkage strain with freezing times
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图 12 径向应变、轴向应变与冻结次数变化关系
Figure 12. Relationship among radial strain, axial strain and freezing times
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图 13 线应变与冻融循环次数关系
Figure 13. Relationship between linear strain and numbers of freeze-thaw cycle
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图 14 膨胀土试样SEM微观结构特征
Figure 14. Microstructural characteristics of expansive soil samples
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图 15 冻结前、后试样孔隙结构状态示意图
Figure 15. Diagram of pore structure state of samples before and after freezing
表 1 试验方案
Table 1 Test programs
试样编号 干密度/(g·cm-3) 含水率/% 饱和度 冻融循环次数 T1 1.60（ρdmax） 17.7 0.70 0，1，2，3，4，5，6，7，8 T2 1.60（ρdmax） 19.7 0.78 T3 1.60（ρdmax） 21.7（wopt） 0.86 T4 1.60（ρdmax） 23.7 0.94 T5 1.60（ρdmax） 25.7 1.00 T6 1.52 17.7 0.62 T7 1.52 19.7 0.69 T8 1.52 21.7（wopt） 0.76 T9 1.52 23.7 0.83 T10 1.52 25.7 0.90 T11 1.44 17.7 0.55 T12 1.44 19.7 0.61 T13 1.44 21.7（wopt） 0.68 T14 1.44 23.7 0.74 T15 1.44 25.7 0.80 T16 1.36 17.7 0.49 T17 1.36 19.7 0.54 T18 1.36 21.7（wopt） 0.60 T19 1.36 23.7 0.66 T20 1.36 25.7 0.71 
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