Reaction principles, deposition and failure mechanisms and theories of biomineralization: progress and challenges
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摘要: 微生物矿化作为地质演变及碳氮循环不可或缺的一环，给岩土、水利及环境等领域带来了新的机遇和挑战，其衍生而来的以MICP为代表的微生物岩土技术已成为环境岩土工程最具革新性的技术领域之一。近20年来，微生物岩土技术从概念验证阶段到相关领域技术示范已取得了重要进展。为推进对该领域更加深入的基础认识与研究，本文系统回顾了MICP技术并针对以下3部分进行了重点阐述：脲酶菌成矿作用的生物化学原理、微生物加固土的沉积模式及加固体破坏机理、涉及生物-化学-水力-力学等多物理场耦合作用下的微生物矿化反应理论。此外，还总结了微生物岩土技术目前亟待解决的问题与挑战，对潜在的研究热点与应用前景进行了探讨和展望。Abstract: The biomineralization is an integral part of geological evolution and carbon-nitrogen cycle, and it has brought new opportunities and challenges in the geotechnical, water conservancy and environmental fields. The inspired bio-geotechnical technology represented by the MICP process has become one of the most innovative technological topics in the environmental geotechnical engineering. In the last two decades, the bio-geotechnical technology has made significant progress from the proof-of-concept phase to the technology demonstration in the relevant environments. In order to promote more comprehensive and in-depth basic understanding and researches on this topic, a systematic review of the MICP technology is performed, focusing on the following three parts: biochemical principles of urease-producing bacteria-induced biomineralization, precipitation patterns and failure mechanisms of bio-cemented soil, and theories of biomineralization reaction under the multi-physics coupling effects of bio-chemo-hydro-mechanical model. Furthermore, the current problems and challenges of bio-geotechnical technology are summarized, and the potential research hot spots and application prospects are discussed.
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0. 引言
土拱效应是岩土工程领域重要的现象，显著影响地层应力传递和变形传播规律，常见于隧道、桩承式路堤、挡土墙等工程[1-5]。基坑工程中，土体开挖会导致坑底地层应力释放并产生不均匀回弹变形，引起土拱效应[6]。
Meng等[7]基于现场实测发现，当基坑开挖深度达到一定值时下方既有隧道上浮量会急剧增大。该现象与坑底土拱效应有关[6]，隧道残余覆土厚度随上方基坑开挖的进行逐渐减小，当土拱松动区发展至隧道范围时，隧道顶部地层竖向应力快速下降且土体松动弱化。此外，为控制既有地下结构变形，上方基坑工程通常采用坑底地层加固、分区开挖等措施[8-9]。这些措施实质上限制了坑底土拱松动区扩展，进而达到了减小地层不均匀变形、降低应力释放的作用。然而，上述措施设计参数依赖经验，包括加固范围、分区开挖尺寸等，因而难以实现变形控制要求[10-11]。以隧道为例，据统计，超过64%的基坑上跨运营隧道工程出现了隧道上浮超限的现象[12]。因此，有必要关注坑底地层的应力转移和变形传播机制，明确坑底土拱效应边界条件、影响范围和演化规律。
实际基坑工程中，因机械土方开挖作业，坑底地层应力和变形测试极为困难，坑底土拱效应的相关研究鲜见报道。离心模型试验可构建均质地层并使用高精度传感器，获取规律性结论，是研究此类问题的重要手段[13-14]。Ng等[15]、Shi等[16]和陈仁朋等[17]在基坑离心模型试验中测试了坑底回弹，但隧道的存在会显著影响结果。刘炀镔等[18]基于离心试验讨论了围护墙插入深度对基坑稳定性的影响，但并未关注坑底土体的应力场和变形场。综上所述，坑底土拱效应的研究尚缺少必要的试验支撑。
本文开展了干砂地层基坑开挖坑底土拱效应离心模型试验和不同开挖深度和宽度的多工况数值模拟。试验和数值分析重点关注坑底竖向应力和回弹变形。本文研究确定了坑底土拱效应边界迹线，揭示了基坑开挖坑底土拱效应形成-演化机制，明确了不同参数的影响规律。研究成果可为预测基坑坑底地层响应和下方既有地下结构变形控制提供支撑。
1. 基坑开挖坑底逆土拱效应
坑底土拱效应如图 1（a）所示，和活动门上方土拱效应（图 1（b））的主要区别在于土拱发展方向和力-位移边界条件。根据发展方向，可将活动门上方自下而上发展的土拱效应定义为“正土拱效应”。坑底土拱效应由上方卸载所致，其发展方向自上而下，与正土拱效应相反，可被定义为“逆土拱效应”。相应的，对于围护墙外侧土体，若存在因墙体变形水平卸载而产生的土拱效应，可被定义为“侧土拱效应”。
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图 1 基坑坑底逆土拱效应和活动门上方正土拱效应示意图Figure 1. Schematic of downward soil arching below excavation base and upward soil arching above trapdoor随活动门下移，正土拱向地表发展演化，其土拱区和松动区边界上均存在摩擦力Ff（土-土界面）作用，阻碍土体向下滑动。与之相对的，坑底逆土拱会随开挖深度加深而逐渐向下发展，且基坑围护结构的存在会显著影响地层中的应力传递机制。逆土拱的侧部（围护墙边）和下部边界（围护墙底）上分别存在摩擦力Ff（土-结构界面）和支承力Fs，二者共同作用，限制了地层应力释放和回弹变形。本文将这种自上而下发展且围护结构影响应力传递的土拱效应定义为坑底逆土拱效应，并将显著受到开挖扰动影响的坑底浅部地层定义为松动区。
2. 离心试验方案
2.1 试验方案
本文开展的干砂地层基坑开挖坑底土拱效应离心试验在浙江大学ZJU-400土工离心机上完成。离心机有效旋转半径为4.5 m，试验过程中离心加速度保持为60g。本模型为左右对称的平面应变模型，图 2给出模型平面布置的示意图。试验用刚性模型箱内部尺寸为1000 mm×400 mm×1000 mm（长×宽×高）。根据相似定律，开挖基坑的模型和原型尺寸如表 1所示，原型基坑深度和宽度分别为24 m和15 m。若无特殊说明，后文中所给数据均为原型尺寸。
表 1 基坑模型与原型尺寸Table 1. Model and prototype dimensions of excavation变量名 模型尺寸/mm 原型尺寸/m 基坑开挖深度 400 24 基坑开挖宽度 250 15 围护墙嵌入深度 200 12 围护墙厚度 25 1.5 模型深度 1000 60 模型宽度 1000 60 2.2 试验材料
福建标准砂被广泛用于土工离心试验[16, 19]，其颗粒组成主要为细粒（图 3）。本试验通过“砂雨法”制备地基土，控制相对密实度为75%。基坑内土体开挖采用“排液法”[15-17]模拟，待开挖土体由ZnCl2重液替代，其实际密度与地基土差别约为2%。试验准备过程中先在开挖范围内贴设厚度为0.5 mm的柔性薄膜，开挖范围底部薄膜设有开孔并通过管路与模型箱外重液收集容器连接，然后在开挖范围内灌入重液。
本试验主要关注基坑坑底地层响应，为确保“排液法”顺利开展并限制围护墙变形，在围护墙外加支撑固定。围护墙和支撑模型均由铝合金材料制成，其杨氏模量约为72 GPa。试验过程围护墙水平位移可以忽略不计。
试验使用LVDT和微型土压计测试坑底回弹和土压力，具体布置如图 2所示。两种传感器精度分别为5×10-3 mm和1 kPa，可以保证测试结果的准确性。此外，其他断面布置了3对弯曲元，具体位置未在图中画出。弯曲元用于测试土体剪切波速，进而获得土体小应变剪切模量G0，结果在表 2给出。
表 2 地基土HSS模型参数Table 2. HSS model parameters for soil参数 数值 参数 数值 Erefoed/MPa 22.8 G0/MPa 86.4 Eref50/MPa 28.6 γ0.7 2×10-4 Erefur/MPa 103.0 einit 0.693 γ/kPa 15.53 K0 0.45 c'/kPa 0 νur 0.2 φ'/(°) 34.4 Rf 0.9 ψ/(°) 4.4 m 0.5 2.3 试验过程及结果
模型制备完成后吊入离心机吊篮。模型箱与重液收集箱通过管道连接，管道中设有电磁控制阀。开启离心机使模型重力加速度达到60g。待传感器示数稳定后，打开电磁阀开关开始排液，排液过程中保持重液流速恒定。试验过程中实时采集所有传感器读数。上机实物图像如图 4所示。
3. 数值分析方案
3.1 基于离心试验的数值模型
为进一步研究坑底逆土拱效应形成-演化机制，采用PLAXIS 2D开展基坑开挖坑底逆土拱效应数值分析。有限元模型基于离心试验原型尺寸建立，地层水力条件为干，模型边界设置为100 m（长）×100 m（宽），远大于2倍开挖范围，边界效应可以忽略。
基坑开挖岩土体的应变量级主要为小应变范围（10-6~10-3）[20]。为考虑土体小应变阶段模量的非线性、应力相关的特点[21]，地基土使用小应变硬化土（HSS）模型。土体本构参数主要由室内单元体试验获得[22]，其中剪切模量取试验时弯曲元测试结果的平均值，具体如表 2所示。因试验中围护墙变形很小，计算时限制围护墙位移为0。
3.2 多工况基坑开挖数值模型
基坑开挖导致的坑底逆土拱效应示意图如图 5（a）所示，Hl和Ha为基坑坑底到松动区和土拱区最大影响范围的竖向距离。基坑开挖深度He和宽度B是坑底逆土拱效应形成-演化的关键影响因素，显著影响拱效应的范围与发挥程度。为研究不同开挖尺度下坑底逆土拱效应的演化规律，共开展了25组模拟计算，各算例地层参数均与前文一致。计算工况如表 3所示，其中围护墙高度Hw均为36 m。
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图 5 坑底逆土拱分区及其演化Figure 5. Division of downward soil arching below excavation base and its evolution表 3 基坑开挖计算工况Table 3. Simulation conditions of excavation变量 数值/m 开挖宽度B 5，15，30，45，60 开挖深度He 6，12，18，21，24 围护墙高度Hw 36 4. 离心试验及数值分析结果
4.1 离心试验结果及数值模型验证
试验前后地层竖向应力的比值是评价应力变化、反映土拱效应发挥程度的重要指标[23-24]。针对坑底逆土拱效应，定义竖向应力比为基坑开挖后某点竖向土压力与开挖前之比。坑内中心线上和围护墙底部的竖向应力比实测结果在图 6，7用实心点表示。图 6所示，坑内竖向应力比小于1，表明开挖后竖向土压力下降，坑底发生应力释放。然而，围护墙底部区域测试结果显示（图 7），开挖后土压力出现明显增大（竖向应力比＞1），这表明坑底存在应力转移现象，证实了坑底逆土拱效应存在。坑底回弹如图 8所示，呈“倒锅底形”，即拱形分布，最大回弹位于基坑中心。
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图 6 基坑中心线上竖向应力比和归一化回弹Figure 6. Vertical stress ratios and normalized ground heave ratios in centerline of excavation为验证模型参数的准确性，将试验实测数据和数值模型的计算结果进行对比，结果显示开挖后坑底地层的响应基本吻合。基坑中心线上的竖向应力比与归一化回弹δ/δmax如图 6所示，竖向应力比的模拟结果略小于实测值。随深度增加，竖向应力比和δ/δmax逐渐增大和减小，最终趋于开挖前的状态。
在土拱效应的相关研究中，应力的拐点标志着地层应力状态的改变，常常被用于确定土拱边界[25-26]。但对于坑底逆土拱效应，竖向应力比随深度持续增加，曲线在数学上不存在拐点。因此，本文基于卸荷单元体试验中临界卸荷比和极限卸荷比以确定土拱区和松动区的高度，即Ha和Hl。既有试验结论显示，干砂地层中极限卸荷比约为0.8[27-28]，当卸荷比小于该值时，扰动效应明显且土体回弹急剧增加。该值对应的
地层竖向应力比为0.2，由此可确定松动区的边界。砂土地层中针对临界卸荷比的研究鲜有报道，因此考虑通过其他方法确定土拱区高度。分层总和法中，砂土地层的计算深度可根据地层应力变化小于20%确定。该深度以下不存在显著的地层相对位移且土体变形忽略不计，可视为坑底逆土拱效应的下边界，对应的地层竖向应力比为0.8。根据上述方法，可确定本模型中松动区和土拱区的最大高度分别为4.6 m和21.6 m。土拱区边界对应的δ/δmax约为20%。
围护墙底部竖向应力比如图 7所示。开挖后，试验和模拟均观测到该处竖向应力比大于1，实测最大竖向应力比为1.2。值得注意的是，PLAXIS 2D中板单元没有厚度，因此仅对围护墙外侧区域进行对比。距基坑较远处，实测竖向应力比减小至小于1，表明该区域出现竖向卸载，而有限元模型不能模拟这一现象。一般认为应力变化小于5%的区域内土拱效应的影响可以忽略不计[25]。此处将竖向应力比大于1.05的部分视为拱脚区，可确定该模型拱脚宽度Ba约为4.7 m，此时拱脚的边界也约为实测竖向应力比连线与竖向应力比为1.0直线的交点。
基坑坑底回弹如图 8所示，模拟结果与实测结果较吻合，均呈“倒锅底”形。坑底地层存在明显差异变形，最大和最小回弹量分别位于基坑中心和靠近围护墙处，差值为31 mm。数值模型中最大回弹量为44.8 mm，略小于实测结果。根据《建筑地基基础设计规范：GB50007—2011》推荐的坑底回弹计算方法[29]，计算的坑底最大回弹量为31.5 mm。该值小于实测值和模拟值，结果偏于危险，这可能与该方法未考虑卸载导致的地基土模量衰减有关。
4.2 坑底土拱分区
图 9给出基坑数值模型中基坑底土体偏应变云图，基坑坑底上方的无关部分已经略去。由前文分析可知，围护墙是坑底逆土拱效应的边界条件之一。基坑开挖后，土-结构界面产生切应力并向坑内传递，导致围护墙侧壁附近出现了显著的偏应变集中带。此外，围护墙底部以下也存在剪切带，其与水平方向的夹角约为61.5°，与主动朗肯状态下滑裂面和水平面的夹角相近（45°+φ/2=61.5°）。
图 10给出基坑数值模型中基坑底土体相对密实度云图。地基土初始相对密实度为75%，开挖后坑底绝大部分区域相对密实度下降且越靠近坑底土体越松散。其中松动区内相对密实度变化最为明显，土拱区其余范围内略有减小，而稳定区基本不变。基于图 10可知，松动区土体显著受到上方卸载和扰动的影响，表现为结构性减弱、力学性能劣化。此时土拱效应难以充分发挥，可能导致下方既有地下结构承受过大附加荷载进而出现变形超限。因此实际工程中有必要重点关注松动区影响范围，控制地下结构间的安全距离。值得注意的是，在围护墙底部，开挖后相对密实度反而增加，该现象由坑底逆土拱效应发挥和地层应力转移所致，与前文中该区域的实测和模拟竖向应力比结论相印证。
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图 10 地层相对密实度分布Figure 10. Distribution of relative density of soil below excavation base图 11给出基坑数值模型中基坑底土体在不同深度处的归一化回弹结果。各剖面的间隔深度为4 m，同一深度处的最大回弹量在右侧给出。随深度增加，开挖后的地层响应减弱，最大回弹量减少，回弹曲线也更加平缓。因围护墙的阻隔作用，回弹主要发生在围护墙内部。值得注意的是，在围护墙内侧及围护墙底部地层（即图 9中偏应变集中带）回弹分布发生明显变化。在活动门上方正土拱效应的研究中，有学者将这种地层应变发生急剧变化的区域视为土拱的边界[31]。
根据前文所述方法，可同时取多个纵向剖面确定松动区和土拱区下边界迹线，如图 12所示。各纵向剖面距离基坑中心的水平距离xp为0，3，6 m，对应确定的松动区高度为4.6，4.1，3.2 m，土拱区高度为21.6，20.0，17.1 m。松动区和土拱区的下边界迹线函数均接近于开口向上的抛物线，其中松动区边界变化更加平缓。可以推测，松动区和土拱区下边界的形状参数与开挖深度He和宽度B密切相关。
4.3 坑底逆土拱效应演化规律
坑底逆土拱效应的演化规律类似于活动门上方正土拱效应。基坑开挖的深度He和宽度B类比于活动门试验中门板的下移量和宽度，二者的大小决定了卸载程度，与土拱效应的范围成正相关[30]。此外，区别于正土拱效应，围护墙深度Hw也会影响土拱的演化机制。坑底逆土拱效应随开挖深度He演化如图 5（b）所示。当开挖深度较浅时，松动区和土拱区范围较小，此时逆土拱效应仅存在于围护墙深度以内。随开挖进一步增加，逆土拱效应向下发展并超过围护墙底部，此时墙底竖向应力增加并产生剪切带。随后，逆土拱效应进一步发展，松动区和拱脚范围随开挖深度增大而逐渐增加。
图 13给出松动区高度随开挖深度变化关系。不同开挖宽度下，松动区高度与开挖深度基本呈线性正相关。此外，开挖宽度对松动区高度也略有影响。减小基坑开挖的深度和宽度有利于控制松动区范围。对各案例结果线性拟合可以得到松动区高度与开挖深度的关系（图 13），根据拟合关系可简单估算坑底的松动区高度约为0.2倍开挖深度。松动区内土体松散、变形显著，实际工程中应尽可能控制该范围与下方既有地下结构的安全距离。需要注意的是，该结论仅适用于干砂地层，不同地层条件下的规律仍有待进一步验证。
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图 13 坑底松动区高度随开挖深度演化规律Figure 13. Evolution of height of loosened zone with increasing excavation depth图 14给出坑底逆土拱高度随开挖深度的关系，图中横纵坐标均基于围护墙高度归一化处理。随开挖深度增加，坑底逆土拱效应产生并向下发展，且其影响范围逐渐增加。不同开挖宽度的基坑坑底均呈现相似的规律。当开挖深度增加至接近围护墙底部时，明显可见土拱区高度的增长趋势变缓。此外，基坑开挖宽度也显著影响了坑底逆土拱效应的发展。相同开挖深度下，逆土拱高度随开挖宽度的增加而增加。值得注意的是，开挖宽度大于30 m时，这种变化不再明显。
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图 14 坑底逆土拱高度随开挖深度演化规律Figure 14. Evolution of height of arching zone with increasing excavation depth由图 12可知，土拱区的下边界迹线函数接近于抛物线。为描述坑底逆土拱效应下边界的形状特征，定义下边界高跨比α=[Ha-(Hw-He)]/(B+2Ba)。如图 15，下边界高跨比α与He/Hw基本呈线性正相关。由此可知，坑底逆土拱效应随开挖深度的增加主要向下部发展而非向两边扩张。当He/Hw为0.374时，拟合直线与横坐标相交，该点表示逆土拱效应发展到围护墙以下的临界状态。为减少基坑开挖对下方地下结构的影响，实际工程中可适当增加围护墙插入深度以减小土拱下边界高跨比，避免土拱区发展至既有地下结构范围。
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图 15 坑底逆土拱下边界高跨比Figure 15. Depth-span ratios of lower boundary of downward soil arching and its evolution with increasing excavation depth5. 结论
本文开展了干砂地层基坑开挖土拱效应离心模型试验及多工况下坑底逆土拱效应数值分析，主要得到以下3点结论。
（1）基坑开挖导致坑底产生土拱效应，地层中存在应力转移和差异变形现象。坑内土压力减小，而围护墙底部土压力增大，最大竖向应力比为1.2。坑底回弹呈拱形分布，最大和最小回弹分别位于基坑中心和靠近围护墙处，差值为31 mm。
（2）坑底逆土拱效应与活动门上方正土拱效应的主要区别在于土拱发展方向和力-位移边界条件。基于土拱效应可将坑底划分为松动区、土拱区和稳定区，松动区内土体相对密实度明显下降。
（3）基坑深度和宽度是影响坑底逆土拱效应形成-演化的关键因素。坑底松动区和土拱区范围与基坑宽度和深度呈正相关，实际工程中应尽量避免松动区发展到坑底下方既有地下结构。减小开挖深度和宽度、增加围护墙插入深度均有利于控制基坑开挖对下方既有地下结构的影响。
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图 1 脲酶菌诱导矿化反应过程概述
Figure 1. Overview of biomineralization process induced by ureolytic bacteria
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图 3 多孔介质中细菌传输、微生物矿化沉积及微生物加固土破坏模式示意图
Figure 3. Schematic diagram of bacterial transport, microbial-mineralization precipitation and failure patterns in biocemented soil
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