强渗透性注浆加固地层蠕变特性及长期变形预测

Creep Behavior and Long-term Deformation Prediction of Ground Reinforced by High-permeability Grouting

摘要

临江平原城市往往具有强渗透性地层、高地下水位，并存在与地下水强烈水力联系的地表水体等先天不利条件，易诱发地下工程渗漏、地表沉降等环境岩土问题。注浆加固技术作为常用的工程治理措施，可有效降低地层渗透性、提升地基承载力，并进一步控制地表沉降。然而，在长期应力‒地下水压耦合作用下，注浆加固地层可能发生显著的蠕变变形甚至是蠕变破坏，严重影响工程在服役期间的安全性与长期稳定性。为系统研究注浆加固地层的蠕变特性及其演化规律，以注浆加固形成的粉砂、砂卵石固结体为研究对象，开展真实水环境下分级加载蠕变试验并分析其蠕变特征。结果表明：随着荷载水平的提高，固结体蠕变速率逐渐增大，蠕变破坏风险逐渐增加。在低应力水平下，固结体主要经历减速、等速蠕变阶段，蠕变量最终趋于某一稳定值；而在高应力水平下，固结体进入加速蠕变阶段，蠕变量明显增加并最终发生蠕变破坏。在此基础上，采用Burgers模型和非线性黏弹塑性蠕变模型对各级荷载下蠕变数据进行拟合及参数识别，结果显示，拟合度均大于95%，表明该模型可准确描述注浆地层固结体的蠕变特性。最后，基于COMSOL Multiphysics开展注浆加固地层长期沉降数值模拟，结果显示，地层沉降量随时间逐渐趋于稳定且始终控制在预警值内，证明工程区域地层经注浆加固治理后具备良好的长期稳定性，预期不会发生沉降破坏。

Abstract

Objective Although grouting reinforcement techniques effectively enhance the bearing capacity of strata in the short term, the grouted bodies are prone to creep deformation under the combined influence of sustained loading and groundwater pressure. This phenomenon can lead to gradual surface settlement and structural instability, compromising the long-term safety and performance of underground infrastructure. This study investigates the creep behavior of grouted bodies formed in highly permeable silt and sand-gravel strata under coupled axial load and hydraulic pressure. The objective is to systematically examine the creep mechanisms and deformation characteristics, providing theoretical support and practical guidance for long-term stability assessment and deformation prediction of grouting-reinforced strata. Methods Firstly, silt and sand-gravel aggregates were collected from in situ formations and packed into molds. A permeation grouting method was employed to simulate field grouting conditions. Following grout injection and initial setting, specimen surfaces were leveled and sealed, and the specimens were cured for 28 days under controlled temperature and humidity. Uniaxial compressive strength tests were then conducted to determine the peak strength of the grouted bodies, which served as a reference for subsequent creep loading schemes. Secondly, creep tests were performed under long-term stepwise loading conditions using a pressurized chamber filled with water to apply confining pressure. Each load increment was maintained until creep deformation approached stabilization, after which the next load level was applied, and this process continued until specimen failure. Full creep curves were recorded throughout the process. The effects of stress level on deformation magnitude and creep rate were evaluated, and the long-term strength of the grouted bodies under coupled stress-seepage conditions was derived using the isochronous stress method. Finally, experimental data were fitted using the Burgers model and a nonlinear viscoelastic-plastic model, and key creep parameters were extracted accordingly. A representative numerical model of the grouted stratum was developed using actual site parameters and was implemented in COMSOL Multiphysics to simulate long-term settlement behavior under coupled mechanical-hydraulic conditions. Results and Discussions The creep tests revealed that the time-dependent deformation behavior of the grouted bodies was strongly stress-dependent, and evident stress thresholds were identified at 2.3 MPa for silt and 3.4 MPa for sand-gravel. Below these thresholds, the specimens mainly exhibited decelerating and steady-state creep, with a gradually decreasing strain rate. In contrast, when the applied stress exceeded the thresholds, accelerated creep occurred, which was characterized by continuously increasing axial strain and eventual failure. Significant increases in total axial strain were observed once the stress surpassed the threshold, from 0.200% to 0.403% in silt and from 0.091% to 0.458% in sand-gravel. These results indicated a substantial risk of secondary failure in grouted strata under sustained high stress and emphasized the necessity of incorporating creep effects in design and long-term performance evaluations. Increased loading not only delayed the onset of steady-state creep but also amplified the long-term creep rate. At stress levels of 1.5 MPa and 1.8 MPa, steady-state creep rates approached zero. However, at 2.3 and 3.4 MPa, steady-state creep rates increased significantly, reaching approximately 0.2×10^‒4/h. This increase in creep rate under high stress conditions exacerbated the risk of long-term instability. The isochronous stress-strain curves displayed a linear trend under low stress conditions and transitioned to nonlinear behavior with distinct inflection points when the stress exceeded the threshold. These inflection points corresponded to the long-term strength limits of the grouted bodies. Comparisons to actual site loading conditions indicated that operational stresses remained below these limits, which indicated that the grouted strata will remain stable over extended service periods. Both the Burgers and nonlinear viscoelastic-plastic models provided accurate fits to the experimental creep data across all stress levels, with coefficients of determination (R²) exceeding 0.95. Post-grouting settlement curves demonstrated the effectiveness of grouting in mitigating short-term deformation. Numerical simulations showed a high initial settlement rate that progressively attenuated over time. After 50 years, settlement magnitudes at monitoring points were 8, 9, 19, and 24 mm, all of which remained below the critical threshold of 25 mm. These findings validated the long-term stability of the grouted strata and confirmed that reactivation of settlement failure was unlikely in treated zones. Conclusions Creep tests under stepwise loading are conducted on grouted bodies formed in highly permeable silt and sand-gravel strata. The results reveal that high stress levels significantly increase creep deformation and pose potential threats to the stability of grouted formations. Therefore, the creep behavior of grouted strata should be thoroughly considered in engineering design and service-life assessment. Numerical simulations incorporating laboratory-derived creep parameters confirm that the treated strata are expected to maintain long-term stability without recurrence of settlement-induced failure.

Graphical abstract

关键词

注浆固结体 / 蠕变试验 / 长期稳定性 / 数值模拟 / 地层沉降

Key words

grouted consolidation body / creep test / long-term stability / numerical simulation / ground settlement

本刊网刊

临江平原城市地下工程大规模渗漏易导致周围岩土体大量流失，引发地层疏松空洞、地表沉降等环境岩土问题^[1]。为有效控制此类病害的发生，工程上常采用注浆加固技术，即向强渗透性地层（例如粉砂、砂卵石层）中注入特定浆液以填充孔隙、裂隙，通过胶结作用将松散土体固结成整体，从而达到改善土体密实度、减小渗流通道、增强地层承载能力的目的^[2‒3]。

作为一种典型的复合材料，注浆加固形成的固结体内部普遍存在软弱结构面^[4]。在长期服役过程中，其力学性能可能会逐渐劣化，尤其在持续应力作用下易表现出显著的蠕变效应。蠕变变形在初期通常不易察觉，但随着时间的推移，其对加固地层的长期稳定性和耐久性影响愈发显著。已有研究指出^[5]，若忽略注浆加固地层的蠕变效应，会低估地层长期沉降变形量。同时，长期处于地下水压作用下，固结体内部损伤持续累积，将进一步降低其长期强度^[6]。因此，尽管注浆固结体初期能够有效提升地层承载力，但在长期应力渗流耦合作用下，仍可能面临蠕变变形引起的潜在破坏风险。为此，深入研究注浆地层固结体的蠕变特性及其演化规律，对于评估注浆加固效果以及保障加固地层长期稳定性具有重要意义。

近年来，国内外学者围绕注浆固结体的蠕变特性开展了大量研究。左永振等^[7]通过坝基注浆固结体蠕变试验证实，胶结作用可使蠕变变形量降低40%～60%；杨爱武等^[8]开展泥浆固化土的分级加载蠕变试验，并建立表征固化土蠕变特征和长期强度的预测公式；张乃烊等^[9]揭示了含水率对不同应力水平下泥质页岩注浆体的影响效果；辛亚军等^[10]通过胶结厚度参数化试验，建立了损伤阈值与胶结界面强度的量化关系。此外，许多学者对固结体的蠕变本构模型进行了创新：徐云飞^[11]和汪涛^[12]在传统Burgers模型中串联弹塑性损伤元件，成功表征了固结体的非线性蠕变响应；刘旸等^[13]结合损伤力学和断裂力学理论，建立了注浆加固体的动态渗流‒蠕变本构模型；Yin等^[14]识别了注浆体蠕变的典型3阶段特征，并基于改进Burgers模型实现了隧道变形的定量预测；段卫党等^[15]结合FLAC^3D反演分析，提出运营期隧道衬砌安全系数的时效衰减方程，并对衬砌变形及安全系数进行了合理预测；尹占超^[16]将干湿循环作为考虑因素，建立了考虑干湿循环作用的非线性黏弹塑性蠕变模型，并分析了注浆隧道典型断面20 a的蠕变位移发展规律。

以上结果为注浆固结体蠕变特性研究提供了重要的理论依据，但目前针对地层‒注浆浆液胶结固结体的蠕变特性研究相对匮乏。此外，多数试验往往采用静态饱水方式模拟岩体含水状态^[17‒19]，难以真实反映其在渗流‒应力耦合作用下的蠕变特性及其演化规律。基于此，本文分别制备地层‒注浆浆液胶结形成的粉砂、砂卵石固结体，开展真实水压作用下分级加载蠕变试验，系统分析其蠕变特征。同时，根据试验结果，选取合适的蠕变本构模型并进行参数辨识，随后将该参数代入COMSOL Multiphysics软件中，以模拟加固区域地表的长期沉降过程。研究成果可为注浆加固地层的长期稳定性评估及变形预测提供一定理论依据和工程指导。

1 试样制备与试验方案

1.1 试样制备

研究依托于某临江城市超大型地下空间工程。该工程三面环水，工程地质与水文地质条件极为复杂，周边地层以富水性强、渗透性高的砂卵石层为主。受前期勘测不足及工程环境复杂性等不确定因素影响，施工过程中出现了地下室突水涌砂、底板变形和地表沉降等多种典型工程灾害。

病害治理期间，对工程周围地层空洞进行了大量注浆加固，主要加固对象为渗透性较强的粉砂层和砂卵石层。地层注浆本质是浆液驱替水和空气的过程，假设土层孔隙完全被浆液充填，为估算制样时浆液用量，先测试一定体积烘干试样在天然堆积状态下的饱和吸水量，结合地勘报告中取芯土样的物理参数，确定粉砂土样和砂卵石土样的孔隙率分别为37%、32%。

试验采用现场收集的粉砂和砂卵石作为骨料，为保证与现场工程条件的相似性，未对其泥质组分进行处理。注浆材料选用与现场施工一致的水泥‒水玻璃双液浆。按照试验设计配比（表1），采用浆液完全浸没土层模拟渗透注浆。首先，将混合均匀的材料分别装入100 mm×100 mm×100 mm的试模中，并逐层捣固以确保密实性。随后，缓慢灌入配制好的浆液，直至浆液溢出可认为达到饱和状态。待浆液凝结后，抹平表面并覆膜保护，置于恒温恒湿环境（(20±2) ℃，(95±1)% RH）中养护28 d。拆模后经试验测定，粉砂和砂卵石固结体的单轴抗压强度分别为2.4 MPa和3.4 MPa。

1.2 试验方案

蠕变试验采用四川大学研发设计的YSL‒200多通道水压‒轴压联合作用岩石流变试验系统，如图1所示。

试验采用三轴条件下的分级加载蠕变方案。试验过程中，将试样放置在充满水介质的承压桶内，通过水施加围压0.5 MPa。蠕变荷载选取轴压分级荷载，各级荷载均在前一级蠕变变形趋于稳定后施加，具体加载方案如图2所示，初始荷载根据试样抗压强度的50%～60%分别确定为1.5、1.8 MPa。

定义应力水平与抗压强度之比为应力百分比。当应力百分比小于80%时，每级增加抗压强度的15%；当应力百分比大于80%时，为防止施加荷载过大导致试样发生突发性破坏^[20]，每级增加抗压强度的8%。

2 蠕变结果

2.1 蠕变曲线

粉砂、砂卵石两种注浆固结体分别经过1 256.4、2 253.0 h加载后，得到分级加载蠕变全过程曲线，如图3所示。基于Boltzmann叠加原理，将该曲线转换为分别加载蠕变曲线，如图4所示。由图3和4可知，固结体在各级应力水平下均发生明显的蠕变变形，蠕变曲线呈阶梯式增长趋势。各级加载瞬间均引发明显的弹性变形，表现为轴向应变的突增。在低应力水平下（除2.5、3.7 MPa外），固结体均表现为稳态蠕变特征，应变率随时间增长逐渐减小，试样由减速蠕变阶段过渡至等速蠕变阶段；在高应力水平下（2.5、3.7 MPa），固结体依次经历减速蠕变阶段和等速蠕变阶段，最终进入加速蠕变阶段，轴向应变量持续增长直至发生蠕变破坏。

上述结果表明，蠕变破坏与应力水平密切相关。粉砂、砂卵石固结体的应力阈值{\sigma }_{\mathrm{s}}分别为2.3、3.4 MPa。当外部应力水平超过该值后，固结体进入加速蠕变阶段，变形速率显著提升，在持续加载作用下最终发生失稳破坏^[21]。

图5为不同轴向荷载下注浆固结体应变的变化规律曲线。由图5可知，注浆固结体初始应变和总应变均随着轴向荷载的增加而增加。其中，初始应变主要反映试样在加载瞬间发生的弹性变形。由于试验采用分级加载蠕变试验方案，随着应力水平的逐级提高，固结体内部微裂纹不断萌生、扩展，导致局部有效承载面积不断减小^[22]，材料内部损伤持续累积，从而在高应力水平下表现出更显著的初始应变。

同时，蠕变变形受应力水平影响显著：在低应力水平下，固结体蠕变应变量增长较为缓慢；在高应力水平下，蠕变应变量明显增加，粉砂固结体由0.200%增大至0.403%，砂卵石由0.091%增大至0.458%。由此可见，应力水平的升高显著加剧注浆固结体的蠕变变形，进而削弱加固地层的整体承载力。

随着外部荷载持续作用，材料内部损伤劣化与变形累积对地层的长期稳定性构成潜在威胁。若服役周期进一步延长，注浆加固地层可能面临二次失稳破坏的风险。因此，应充分重视注浆加固地层蠕变效应带来的潜在不利影响。

2.2 不同应力水平对注浆固结体蠕变速率的影响

等速蠕变阶段是注浆固结体趋于稳定的关键阶段，当该阶段的蠕变速率长时间保持在某一稳定值时，表明注浆固结体内部结构趋于稳定，基本不会发生蠕变破坏^[22]。由于高应力水平下的蠕变速率明显高于低应力水平阶段，故不再展示，仅绘制低应力水平下固结体的蠕变速率变化曲线，如图6所示。由图6可知，两种固结体在不同低应力水平下的蠕变速率均呈初期快速下降，后期逐渐趋于稳定变化的特征。随着外部荷载水平的提高，颗粒间局部应力不断重新分布，微结构持续调整，导致试样从减速蠕变阶段过渡到等速蠕变阶段的时间延长，呈现更强的衰减蠕变特征。当固结体进入等速蠕变阶段，其蠕变速率随着荷载水平的提高逐渐增加。两种固结体在1.5、1.8 MPa应力水平下，等速蠕变速率近似为0；在2.3、3.4 MPa应力水平下，等速蠕变速率达到0.2×10^-4/h。综上，外部荷载水平的提高不仅会延缓固结体进入稳态蠕变阶段的时间，还会提高固结体的长期蠕变速率，进而增加注浆加固地层发生蠕变破坏的潜在风险。

2.3 注浆固结体的长期强度

由上述分析可知，注浆加固后形成的地层固结体受流变机制影响，当外部荷载分别为2.5、3.7 MPa时，粉砂、砂卵石固结体可能发生蠕变破坏。因此，需要获得注浆固结体在水压轴压耦合作用下的长期强度，以此判断注浆加固地层的稳定性和安全性。

长期强度是衡量材料在持续荷载作用下保持稳定的时间效应指标，大量研究表明，岩石长期强度一般低于其瞬时抗压强度^[23‒25]，是预测工程稳定性的重要依据。

采用等时应力法绘制不同轴压下的等时应力‒应变曲线^[25‒26]，如图7所示。

由图7可以看出：在低应力水平的条件下，固结体的等时应力‒应变曲线基本呈现出线性特征，整体分布近似为直线簇。随着应力水平的进一步提高，当其超过应力阈值（2.3、3.4 MPa）时，曲线由线性转换为非线性，并且出现明显的拐点，此时，蠕变机制由黏弹性向黏塑性转变^[27‒28]，固结体内部的损伤加剧，承载能力显著下降，蠕变应变呈现出非线性增长趋势，直至发生宏观失稳破坏。综上所述，粉砂固结体、砂卵石固结体在水压‒轴压耦合作用下的长期强度分别为2.3、3.4 MPa。

本文研究区域地处繁华的城市中心，交通动荷载大，周围既有建筑物荷载高。地表建筑荷载约200 kPa；道路车辆集中荷载最大按700 kPa估计，车辆动荷载冲击系数取1.3～2.0。经过计算，粉砂、砂卵石地层实际承受的最大荷载分别约为1.9、2.3 MPa，小于上述分析的长期强度，因此注浆加固地层不会发生蠕变破坏，该地层在水压‒轴压耦合作用下具备良好的长期稳定性。

3 蠕变模型与参数识别

3.1 蠕变模型

根据上述分析，固结体的蠕变特性在应力阈值前后表现出显著差异。当外部应力低于应力阈值时，固结体处于稳定蠕变阶段，应变率基本保持某一常数，蠕变变形随时间持续增加，表现出软岩类材料的典型时效性特征^[21]。当外部应力超过应力阈值时，固结体进入不稳定的加速蠕变阶段，蠕变速率急剧增加，需要在原有Burgers模型中串联一个非线性黏塑性元件。

参考既有的蠕变相关研究^[21‒22,27]，当应力水平小于阈值时，采用式（1）所示的Burgers模型描述固结体的减速、等速蠕变阶段；当应力水平大于阈值时，采用式（2）非线性黏弹塑性蠕变模型描述固结体的减速、等速、加速蠕变阶段：

{\epsilon }_{\mathrm{1}}(t)=\frac{\sigma }{E_{\mathrm{m}}}+\frac{\sigma }{{\eta }_{\mathrm{m}}}t+\frac{\sigma }{E_{\mathrm{k}}}\left(\mathrm{1}-{\mathrm{e}}^{-\frac{{\mathrm{E}}_{\mathrm{k}}\mathrm{t}}{{\mathrm{\eta }}_{\mathrm{k}}}}\right)（1）

{\epsilon }_{\mathrm{1}}(t)=\frac{\sigma }{E_{\mathrm{m}}}+\frac{\sigma }{{\eta }_{\mathrm{m}}}t+\frac{\sigma }{E_{\mathrm{k}}}\left({}^{\mathrm{1}-e^{-\frac{E_{\mathrm{k}}t}{{\eta }_{\mathrm{k}}}}}\right)+\frac{\sigma -{\sigma }_{\mathrm{s}}}{{\eta }_{\mathrm{0}}}(t-t_{\mathrm{F}}{)}^n（2）

式（1）、（2）中：{\epsilon }_{\mathrm{1}}为轴向应变；E_{\mathrm{k}}、E_{\mathrm{m}}分别为凯尔文体和马克斯威尔体弹性元件的弹性系数；{\eta }_{\mathrm{k}}、{\eta }_{\mathrm{m}}、{\eta }_{\mathrm{0}}分别为凯尔文体、马克斯威尔体、非线性黏塑性模型的黏滞系数；t为蠕变时间；\sigma为蠕变荷载；{\sigma }_{\mathrm{s}}为应力阈值，根据前文蠕变结果，分别取2.3、3.4 MPa；t_{\mathrm{F}}为加速蠕变的启动时间，根据蠕变曲线轴向应变率，粉砂、砂卵石固结体分别确定为83、237 h；n为流变指数，反映固结体发生加速蠕变的快慢程度，n值越大，加速蠕变阶段越快。相应的蠕变模型示意图如图8所示。

3.2 蠕变参数识别

采用Levenberg‒Marquardt非线性最小二乘算法对固结体蠕变模型进行拟合及参数识别，拟合结果如图9所示，参数识别结果见表4、5。

由图9及表4、5可以看出，两种固结体在各级荷载水平下拟合效果较好，拟合优度R²均大于0.95，上述两种模型能够较为准确地描述注浆地层固结体的蠕变特性。

4 地层长期稳定性数值模拟

注浆加固后，地层需要承受地下水压力、地面建筑荷载及车辆荷载等的共同作用，形成了典型的流固耦合问题^[29‒30]，其长期稳定性直接影响注浆加固质量。本文基于COMSOL Multiphysics多物理场数值模拟软件，结合室内蠕变试验进行地层长期变形的预测。

4.1 流固耦合控制方程

为研究方便，作出以下假设^[31‒34]：土体均匀、连续、各向同性；土粒不可压缩；地下水渗流符合达西定律且多孔介质变形等于孔隙变形；孔隙水压力和土骨架之间满足修正Terzaghi有效应力原理。流固耦合的控制方程见式（3）：

\left\{\begin{array}{l}{\rho }_{\mathrm{w}}S\frac{\partial p_{\mathrm{w}}}{\partial t}+\nabla ·{\rho }_{\mathrm{w}}\left[-\frac{k}{\mu }\left(\nabla p_{\mathrm{w}}+{\rho }_{\mathrm{w}}g\right)\right]=Q_{\mathrm{m}},\\ \frac{\partial }{\partial x_j}\left({\sigma }_{ij}^{\mathrm{\text{'}}}-{\alpha }_{\mathrm{b}}{\rho }_{\mathrm{w}}{\delta }_{ij}\right)+\left[\left(\mathrm{1}-\varphi \right){\rho }_{\mathrm{s}}+\varphi {\rho }_{\mathrm{w}}\right]g_i=\mathrm{0},\\ S=\varphi {\chi }_{\mathrm{w}}+\frac{{\alpha }_{\mathrm{b}}-\varphi }{K_{\mathrm{s}}},\\ Q_{\mathrm{m}}=-{\rho }_{\mathrm{w}}{\alpha }_{\mathrm{b}}\frac{\partial {\epsilon }_{\mathrm{v}}}{\partial t}\end{array}\right.（3）

式中：p_{\mathrm{w}}为孔隙水压力，MPa；S为储水系数，1/MPa；{\rho }_{\mathrm{w}}\mathrm{、}{\rho }_{\mathrm{s}}分别为流体密度、固体颗粒密度，kg/m³；Q_{\mathrm{m}}为质量源项，kg/(m³·s)；{\sigma }_{ij}^{\mathrm{\text{'}}}为有效应力，MPa；{\alpha }_{\mathrm{b}}为Biot系数，岩土材料近似取1^[35]；{\delta }_{ij}为Kronecker数，当i=j时取值为1，反之为0；\varphi为孔隙度；k为渗透率，m²；\mu为流体黏度，Pa·s；{\epsilon }_{\mathrm{v}}为体积应变；{\chi }_{\mathrm{w}}为水的压缩系数，取8.81×10^-11 1/MPa；K_{\mathrm{s}}为固体颗粒体积模量，MPa；x_j为第j个坐标方向上的空间坐标分量，m；g_i为重力加速度在第i个坐标方向上的分量，m/s²。

4.2 模型建立与边界条件

根据现场实际工程参数，建立地下工程及周围岩土体的二维对称数值模型，如图10所示。模型尺寸为50.0 m×21.6 m（长×高），土层从上至下依次为杂填土、粉质黏土、粉土、粉砂固结体、砂卵石固结体，模型相关物理力学参数见表6。

边界条件分为应力边界条件和渗流边界条件。应力边界条件中，底部施加固定约束，左侧为对称边界，右侧采用辊支撑以限制水平位移，上部按照实际工程条件施加最大荷载1.6 MPa。渗流边界条件中，以抗浮水位272 m处的土层作为0孔隙水压边界，模型顶部、底部及右侧均设置为无流动边界，结构内部设置为0压力边界。

为简化计算，只考虑注浆加固地层粉砂层和砂卵石层的蠕变特性，其余土层采用摩尔-库伦本构模型。假定体积模量不变，将两种固结体在最大荷载（1.9、2.3 MPa，实际工程中最大荷载（1.6 MPa）加上土体自重荷载）下的蠕变参数转换为三维蠕变参数^[16]，具体见表7。

4.3 模拟结果

采用超细化自由三角形单元对模型区域进行网格划分，并对注浆加固层进行局部网格加密，以提高计算精度。在开展地层长期变形模拟前，先进行初始地应力平衡计算，以确保初始应力场的合理性。地应力平衡后地层位移如图11所示，平衡后土层的位移量级为10^-12，自重影响可忽略不计。

为评估注浆加固对地层沉降的控制效果，对工程区域注浆前后地表沉降变化进行了长期现场监测，结果如图12所示。

工程区域自监测起在大约第315 d实施注浆加固。由图12明显看出，注浆加固后，地表沉降曲线整体呈上移趋势且沉降速率逐步降低，说明注浆加固有效改善了地层变形特性，进一步抑制了地表沉降发展速率。

图13为注浆加固后现场沉降监测与数值模拟结果对比情况。由图13可知，注浆加固初期由于地层固结体尚未充分形成，且模拟采用的蠕变参数来源于养护一定时间后的试验数据，导致模拟结果与初期实测值存在一定偏差。随着时间推移，注浆固结体逐步水化硬化，强度持续增强，模拟值与实测值之间的误差明显减小，整体拟合度较高，表明所构建的数值模型能够较为准确地反映注浆加固地层的沉降演化规律，可用于地层长期变形的预测分析。

基于上述分析，进一步绘制了研究区域地表长期沉降预测曲线，如图14所示。由图14可知，地表初期沉降速率较高，随后逐步减缓，整体呈衰减趋势。预测结果显示，50 a后各监测点的沉降量依次为8、9、19、24 mm，最大沉降量均未超过预警值25 mm。

综上所述，注浆加固措施不仅在短期内能够有效抑制地层沉降的发展，在长期服役条件下仍可保持较好的控制效果。注浆治理后，地层具有良好的长期稳定性，已治理区域预计不会再次发生地层沉降破坏。

5 结 论

1）注浆固结体蠕变行为受应力水平影响显著：在低应力水平下经历减速、等速蠕变阶段，表现为稳态蠕变特征，蠕变量缓慢增长并最终趋于稳定；而在高应力水平下，固结体最终进入加速蠕变阶段，蠕变机制由黏弹性流动转换为黏塑性流动，蠕变应变呈现出非线性增长趋势直至失稳破坏。

2）当试样处于等速蠕变阶段时，蠕变速率随应力水平的提高逐渐增加，高应力水平下固结体呈现出更强的衰减蠕变特性，蠕变破坏风险增加。当外部应力超过应力阈值时，注浆固结体的蠕变应变量远远高于前几级荷载下的应变量，此时蠕变变形对加固地层长期稳定性构成潜在威胁。

3）采用Burgers模型和非线性黏弹塑性蠕变模型对试样蠕变结果进行拟合及参数识别，结果表明，各级应力水平下拟合度均超过95%，表明上述蠕变模型能够准确描述注浆地层固结体的蠕变特性。

4）粉砂、砂卵石地层实际承受的最大荷载分别约为1.9、2.3 MPa，均小于其在水压‒轴压耦合作用下的长期强度极限值（2.3、3.4 MPa），因此注浆加固地层不会发生蠕变破坏。同时，数值模拟结果进一步表明，在长期服役荷载作用下，注浆加固地层沉降量逐渐趋于收敛，均低于沉降预警值，表明注浆加固措施可有效提升地层长期稳定性，预计治理区域不会再次发生沉降破坏。

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基金资助

云南省科技厅科技计划项目(202303AA080004)