Characteristics of cumulative plastic strain and critical dynamic stress of frozen clay under principal stress rotation
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摘要: 冻土作为寒区工程的基础和人工冻结工程的支护壁，经常承受动荷载的扰动，研究其在动荷载作用下累积塑性应变和临界动应力特性，可为寒区工程和人工冻结工程变形控制和稳定评价提供重要参考。为揭示主应力轴旋转对冻结黏土累积塑性应变和临界动应力特性影响，采用冻土空心圆柱仪进行了一系列考虑围压影响的动三轴试验和纯主应力轴旋转试验，分析了冻结黏土累积塑性应变、累积塑性应变率和临界动应力特征变化。研究表明，冻结黏土试样轴向累积塑性应变随着循环次数的增多而增大，围压的增大则会抑制冻结黏土轴向累积塑性应变发展速度，而主应力轴旋转效应会加快冻结黏土轴向累积塑性应变发展速度。冻结黏土轴向累积塑性应变率呈现3种不同变化趋势，提出了基于累积塑性应变速率判别的冻结黏土塑性变形行为划分准则，并建立了冻结黏土塑性安定和塑性蠕变临界动应力表达式，证实了主应力轴旋转条件下冻结黏土临界动应力显著降低。研究结果对冻土工程的设计、施工、稳定评价和寒区资源开发都具有重要的指导意义。Abstract: As the foundation of cold region projects and the supporting wall of artificial freezing projects, the frozen soil often bears the disturbance of dynamic loads. Studying the cumulative plastic strain and the critical dynamic stress under the dynamic loads provide an important reference for the deformation design and stability evaluation of the cold region and artificial freezing projects. To reveal the influences of the principal stress rotation on the cumulative plastic strain and the critical dynamic stress characteristics of the frozen clay, a series of dynamic triaxial tests and pure principal stress rotation tests considering the influences of confining pressure are carried out by FHCA-300, and the characteristics of the cumulative plastic strain, the cumulative plastic strain rate and the critical dynamic stress of the frozen clay are analyzed. The results show that the axial cumulative plastic strain of the frozen clay increases with the increase of cycles, the increase of the confining pressure will restrain the development of its axial cumulative plastic strain, and the principal stress rotation will accelerate the development of its axial cumulative plastic strain. The evolution of the axial cumulative plastic strain rate of the frozen clay shows three different trends. The division criterion of plastic deformation behavior of the frozen clay based on the cumulative plastic strain rate is proposed, and the expressions for the critical dynamic stress of the plastic shakedown and plastic creep of the frozen clay are established. It is confirmed that the critical dynamic stress of the frozen clay decreases significantly under the rotation of the principal stress axis. The research results are of important guiding significance for the design, construction and stability evaluation of the frozen soil projects and the development of the resources in cold regions.
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0. 引言
中国大规模的基础设施建设工程每年产生大量的建筑垃圾，建筑垃圾可通过破碎、清洗、筛分、分级等二次处理后生产出再生骨料[1-2]。再生骨料可用于道路铺筑、工程回填、地基加固等岩土工程领域[3-4]。
强夯碎石桩因其具有提高地基承载力、减小地基沉降和加速地基固结排水等优点常应用于软土地基加固中，施工工序如图 1所示：首先将钢套筒打至设计深度并筒内清泥，套筒内分层填入碎石并使用夯锤夯实，上拔套筒一定高度并再次填料和夯实，直到形成串珠状的散体桩复合地基[5]。许多学者对碎石桩的承载性能、荷载传递、破坏模式等进行了研究[6-8]。受桩长、桩周土体、加载方式的影响，碎石桩可能出现的破坏有3种：鼓胀破坏、刺入破坏和剪切破坏。基于有限单元法和有限差分法等已广泛应用于碎石桩宏观特性的研究[9-10]，然而碎石桩由散体材料组成，连续方法不能准确地模拟其特性。
通过建立三维离散-连续耦合数值模型对再生骨料强夯桩的承载性能进行模拟，研究了再生骨料强夯桩的承载变形机理、桩体破坏模式及荷载传递规律。并分析了不同桩长和不同孔隙率的再生骨料强夯桩的承载性能。以期能为再生骨料强夯桩的推广应用提供参考。
1. 离散-连续耦合数值模型
1.1 数值模型建立
再生骨料强夯桩按图 1所示方法进行成桩，具体细节详见文献[11]。试验选用的再生骨料相对质量密度为2.62，内摩擦角为39度，粒径范围为0.6~9.5 mm，桩周土体为天津路基地表土，相对质量密度为2.65，厚度为60 cm，含水率为15%，土体黏聚力为20 kPa，内摩擦角为32度。成桩后桩长为60 cm，桩径为6 cm。成桩完成后进行加载试验，采用位移加载的方式施加荷载，加载速度为1 mm/min，加载至5 cm时停止加载。
采用FLAC-PFC耦合方法进行承载模拟，如图 2（a）所示，耦合数值模型包括3部分：有限差分模型（桩周土）、离散元模型（散体桩）和耦合墙。模型的建立步骤与室内模型试验一致，分为土基填筑、成桩和加载三步。首先建立桩周土的有限差分模型，采用的本构模型为莫尔-库仑，所用参数见表 1，接下来先把散体桩区域进行挖空，然后在桩底、桩顶和桩侧生成墙形成封闭区域使得颗粒在此区域内生成，桩底墙直径为25 cm，桩顶墙直径为6 cm，桩侧耦合墙直径为6 cm、高为60 cm，颗粒之间采用抗转动线性接触模型（rrlinear model），颗粒细观参数通过直剪试验进行标定后列于表 2。
表 1 土体参数Table 1. Parameters of soilsc/kPa ϕ/(°) E/MPa ν ρ/(g⋅cm-3) 20 32 10 0.4 1830 表 2 再生骨料标定参数Table 2. Calibration parameters of recycled aggregates接触类型 Ball-ball Ball-wall 有效模量E*/Pa 2.0×107 5.0×107 刚度比k* 1.5 1.5 抗转动摩擦系数μr 0.5 — 摩擦系数μ 0.5 0.5 阻尼比 0.7 0.7 孔隙比 0.86 — 最后在再生骨料强夯桩上方生成与桩径相同的加载板，以1 mm/min的恒定速率对碎石桩进行轴向加载，直至位移达到5 cm。如图 2（b）所示，在桩内布置19个测量圆，球体中心垂直位置位于-3~-57 cm处（土表z=0），获得测量圆内应力状态（轴向和径向应力）和微观特征（孔隙率和配位数）。在桩周土有限差分模型中布置21个监测节点，获取连续-离散界面节点处的侧向变形。
1.2 数值模型验证
图 3（a）为模型试验与数值模拟的荷载-沉降曲线对比图，两者曲线变化趋势相同，吻合程度较好。从图 3可以看出，在加载初期沉降达到5 mm之前曲线基本呈线性增加，桩顶应力在较小的沉降量下即迅速增加到约750 kPa；当沉降超过10 mm时，非线性变形明显发展；当桩顶应力超过1500 kPa后沉降迅速发展，沉降超过20 mm后p-s曲线几乎竖直，预示着再生骨料强夯桩丧失了承载能力。
图 3（b）为模型试验与数值模拟的桩体径向变形对比图，从图中可以看出，两者曲线整体变化趋势相同，桩体径向变形都主要发生在桩身20 cm（约3倍桩径）及以上，桩身20 cm以下变形较小，最大变形量均为9 mm左右，桩体呈现上部凸出中下部小的形态。
图 3（c）为模型试验与数值模拟的桩身应力传递系数对比图，两条曲线均为桩体最终破坏时测得，从图中可以看出随埋深增加应力传递系数逐渐减小，超过3倍桩径后传递系数均小于0.2，表明大部分荷载均由碎石桩上部承担，模拟和试验具有较好的一致性。数值模拟中上部第一个和第二个数据监测点异常减小是因为此时颗粒大部分被加载板下压，在测量球中的颗粒较少，所以其平均应力较小使得传递系数较小。
2. 结果分析
2.1 桩周土变形和应力
图 4给出了不同桩顶沉降下（18，34，50 mm）桩周土体的变形和应力云图。从图 4（a）可以看出桩体压缩主要产生在桩体上部，随着沉降增加该段区域内碎石产生剧烈鼓胀变形，从而引起桩周土体产生水平位移。土体水平应力在桩体鼓胀导致的水平挤压下增长剧烈。
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图 4 不同沉降下桩周土变形和应力Figure 4. Deformations and stresses of soil around column under different settlements图 4（b）显示桩周上部土体附近产生了较大的竖直应力增量，增加的竖向应力主要由桩侧摩阻力及变形后的桩体与土体挤压产生，并通过土体剪应力以一定扩散角度传递到远离桩体的土体区域。图 4（c）显示桩周土体在靠近桩体压缩段也出现了较大的竖向位移，但位移量明显小于碎石沉降量。因此可以判断在桩体压缩强烈的范围内，桩体和桩周土体产生了较大相对位移。加载结束后土地表面产生了明显的隆起。
图 4（d）为不同沉降下桩周土体剪切应变分布，土体剪切应变大小直接反映桩体变形对土体的扰动强弱。随着桩体沉降量的增加，土体剪切扰动区域在桩体水平鼓胀推动下向四周扩展，最终观察到贯通地表的连续剪切滑动面。
2.2 桩体变形和应力
图 5（a）为不同沉降时桩体鼓胀变形沿桩身分布图，桩体鼓胀变形整体呈现上部突出中下部小的形态。随着沉降增加鼓胀变形逐渐增加，主要鼓胀变形发生在桩体3倍桩径的埋深范围内，径向应变最大为14%，最大鼓胀变形位置大约在1.5倍桩径处。图 5（b）为桩体水平应力沿桩身分布图，从图中可以看出水平应力随沉降增大而增大，随埋深增大发生较大衰减。与径向应变变化规律一致。
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图 5 不同沉降下桩体变形和应力Figure 5. Column deformations and stresses under different settlements图 6显示了再生骨料颗粒在不同沉降下接触力的分布。随沉降增大，桩顶处直接承受荷载的强接触力链越来越明显，且其接触力值越来越大。接触力链主要集中在桩体的上部，大概3倍桩径深度内，这与径向应变一致。在加载过程中，强接触力链承担桩顶荷载后再通过若干弱接触力链向下部及桩周土体传递荷载。
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图 6 不同沉降下颗粒间接触力链Figure 6. Contact force chains between particles under different settlements2.3 破坏模式
再生骨料强夯桩的破坏模式示意图如图 7所示。随着荷载的增加，再生骨料强夯桩最大鼓胀变形（1.5倍孔径）附近的土体首先进入屈服状态，接下来的荷载会使石柱产生较大的鼓胀变形并挤压石柱周围土体，造成土体塑性区以半球形式向周边扩展。随着荷载继续增加，桩周土体在桩体鼓胀变形的挤压下形成贯通地表的连续滑裂面，地表发生隆起变形，影响范围约为18 cm（3倍桩径）。桩体则最终因为鼓胀段（3倍桩径）径向应变无法限制而丧失承载力。
3. 参数分析
3.1 桩体长度的影响
其他条件不变，只改变桩体长度，得到不同长度下再生骨料强夯桩的荷载-沉降曲线如图 8所示。可以看出桩长过小时，再生骨料强夯桩的承载力很低，只有540 kPa，在桩顶沉降20 mm时便发生破坏，破坏形式为刺入破坏。随着桩长的增加，承载力逐渐提高。桩长7d时与全长桩（10d）时承载力接近，这说明全长桩底部3倍桩径并不承担荷载，有效长度为7d。从5d开始，再生骨料强夯桩发生鼓胀破坏。
3.2 孔隙率的影响
其他条件不变（桩长为10d），只改变孔隙率，得到不同孔隙率下再生骨料强夯桩的荷载-沉降曲线如图 9所示。
随着孔隙率减小，再生骨料强夯桩的承载性能逐渐提高。在孔隙率为0.3，0.35时，曲线随着沉降增加先为线性增加，然后快速发展，最后曲线趋于竖直，而孔隙率为0.4，0.45，0.5时，曲线近似线性变化，原因是桩体孔隙率较大时，颗粒间咬合力较弱，颗粒向桩周土位移时，桩周土能提供较强的侧限作用，当增加到一定沉降后，桩体被压密，此时颗粒不断挤向土体，因侧限作用失效产生破坏。
4. 结论
通过建立三维离散-连续耦合数值模型对再生骨料强夯桩的承载性能进行模拟，研究了再生骨料强夯桩的的承载变形机理、桩体破坏模式及荷载传递规律。并分析了不同桩长和不同孔隙率的再生骨料强夯桩的
承载性能。主要得到以下3点结论。
（1）桩周土体受颗粒挤压变形导致桩体上部位置位移和应力发展迅速。在水平方向表现为鼓胀变形，在竖直方向上地表会有隆起和抬升。鼓胀变形主要集中在3倍桩径范围内。
（2）竖向荷载使桩体产生较大的鼓胀变形并挤压石柱周围土体，造成土体塑性区以半球形式向周边扩展。随着荷载继续增加，桩周土体在桩体鼓胀变形的挤压下形成贯通地表的连续剪切滑裂面。
（3）桩长小于3d，桩体发生刺入破坏，大于3d时发生鼓胀破坏。全长桩底部3倍桩径并不承担荷载，有效长度为7d。随着孔隙率减小，再生骨料强夯桩的承载性能逐渐提高。
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图 1 冻土空心圆柱仪（FHCA-300）结构简化图
Figure 1. Simplified structural diagram of frozen hollow cylinder apparatus (FHCA-300)
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图 5 动三轴试验中不同围压下轴向累积塑性应变随循环次数变化曲线
Figure 5. Variation of axial cumulative plastic strain with cycle times under different confining pressures in dynamic triaxial test
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图 6 纯主应力轴旋转试验中不同围压下轴向累积塑性应变随循环次数变化曲线
Figure 6. Variation of axial cumulative plastic strain with cycle times under different confining pressures in principal stress rotation
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图 7 不同加载方式下轴向累积塑性应变随循环次数变化曲线
Figure 7. Variation of axial cumulative plastic strain with cycle times under different loading modes
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图 8 基于累积应变速率的土体塑性变形行为划分方法
Figure 8. Division method for plastic deformation behavior of soil based on cumulative strain rate
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图 9 =700 kPa时动三轴试验中轴向累积塑性应变率随累积塑性应变变化曲线
Figure 9. Variation of axial cumulative plastic strain rate with axial cumulative plastic strain in dynamic triaxial tests at =700 kPa
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图 10 =700 kPa时纯主应力轴旋转试验中轴向累积塑性应变率随轴向累积塑性应变变化曲线
Figure 10. Variation of axial cumulative plastic strain rate with axial cumulative plastic strain in principal stress rotation tests at =700 kPa
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图 11 冻结黏土不同塑性行为下轴向累积塑性应变速率变化
Figure 11. Variation of axial cumulative plastic strain rate of frozen clay under different plastic behaviors
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图 12 不同加载方式下动剪应力比与围压关系
Figure 12. Relationship between dynamic stress ratio and confining pressure under different loading modes
表 1 试验用土的基本物理参数指标
Table 1 Basic physical properties of testing soil
颗粒相对质量密度Gs 最大干密度
ρdmax/(g·cm-3)饱和含水率wsat/% 液限wP/% 塑限wL/% 塑性
指数2.71 1.72 18.6 34.5 13.9 20.6 
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表 2 试验方案
Table 2 Test schemes
试验
名称试样
编号围压/
kPa动剪应力比CSR 动三轴试验 1~5 400 2.500 2.813 3.125 3.438 3.750 6~10 700 1.429 1.607 1.786 1.964 2.143 11~15 1000 1.000 1.125 1.250 1.375 1.500 纯主应力轴旋转试验 16~20 400 2.500 2.813 3.125 3.438 3.750 21~25 700 1.429 1.607 1.786 1.964 2.143 26~30 1000 1.000 1.125 1.250 1.375 1.500
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表 3 不同类型土塑性响应方式的应变速率划分标准对比
Table 3 Comparison of strain rate classification criteria of plastic response modes for different soils
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表 4 试验土样变形状态统计表
Table 4 Deformation states of test soil samples
围压
σ3/kPa动剪应力幅值qamp/kPa CSR 动三轴试验 主应力旋转试验 试样编号 状态 试样编号 状态 400 2000 2.500 1 塑性安定 16 塑性蠕变 2250 2.813 2 塑性安定 17 增量破坏 2500 3.125 3 塑性蠕变 18 增量破坏 2750 3.438 4 增量破坏 19 增量破坏 3000 3.750 5 增量破坏 20 增量破坏 700 2000 1.429 6 塑性安定 21 塑性安定 2250 1.607 7 塑性安定 22 塑性蠕变 2500 1.786 8 塑性安定 23 增量破坏 2750 1.964 9 增量破坏 24 增量破坏 3000 2.143 10 增量破坏 25 增量破坏 1000 2000 1.000 11 塑性安定 26 塑性安定 2250 1.125 12 塑性安定 27 塑性蠕变 2500 1.250 13 塑性安定 28 增量破坏 2750 1.375 14 塑性蠕变 29 增量破坏 3000 1.500 15 增量破坏 30 增量破坏
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