Coupled multiphysical model for investigation of influence factors in the application of microbially induced calcite precipitation

The study presents a comprehensive coupled thermo-bio-chemo-hydraulic(T-BCH)modeling framework for stabilizing soils using microbially induced calcite precipitation(MICP).The numerical model considers relevant multiphysics involved in MICP,such as bacterial ureolytic activities,biochemical reactions,multiphase and multicomponent transport,and alteration of the porosity and permeability.The model incorporates multiphysical coupling effects through well-established constitutive relations that connect parameters and variables from different physical fields.It was implemented in the open-source finite element code OpenGeoSys(OGS),and a semi-staggered solution strategy was designed to solve the couplings,allowing for flexible model settings.Therefore,the developed model can be easily adapted to simulate MICP applications in different scenarios.The numerical model was employed to analyze the effect of various factors,including temperature,injection strategies,and application scales.Besides,a TBCH modeling study was conducted on the laboratory-scale domain to analyze the effects of temperature on urease activity and precipitated calcium carbonate.To understand the scale dependency of MICP treatment,a large-scale heterogeneous domain was subjected to variable biochemical injection strategies.The simulations conducted at the field-scale guided the selection of an injection strategy to achieve the desired type and amount of precipitation.Additionally,the study emphasized the potential of numerical models as reliable tools for optimizing future developments in field-scale MICP treatment.The present study demonstrates the potential of this numerical framework for designing and optimizing the MICP applications in laboratory-,prototype-,and field-scale scenarios.

A comparative study of using two numerical strategies to simulate the biochemical processes in microbially induced calcite precipitation

In this study,we carried out a comparative study of two different numerical strategies for the modeling of the biogeochemical processes in microbially induced calcite precipitation(MICP)process.A simplified MICP model was used,which is based on the mass transport theory.Two numerical strategies,namely the operator splitting(OS)and the global implicit(GI)strategies,were adopted to solve the coupled reactive mass transport problems.These two strategies were compared in the aspects of numerical accuracy,convergence property and computational efficiency by solving the presented MICP model.To look more into the details of the model,sensitivity analysis of some important modeling parameters was also carried out in this paper.

The Reduction of the Permeability of a Lateritic Soil through the Application of Microbially Induced Calcite Precipitation

Lateritic soils are frequently utilised in tropical areas of the developing world as an engineering material in the construction of rural earth roads, usually in the form of engineered natural surface (ENS) roads. The heavy, seasonal rainfalls common to the tropics results in ENS roads becoming quickly saturated with rainwater, and no longer accessible to motorised transportation. Microbially induced calcite precipitation (MICP) has been successfully used as a treatment process to decrease the permeability of clean, cohesionless sands by studies trying to impede the movement of groundwater, and any pollutants they may contain. In order to see if MICP treatment can also reduce the susceptibility of ENS road lateritic soils to rainwater saturation, this study has treated a Brazilian sample extracted from an ENS road in Espirito do Santo, Brazil, using the MICP bacterium Sporosarcina pasteurii contained within a urea-calcium chloride solution inoculum. Investigation, by means of a Rowe cell, of the post-treatment permeability, to untreated control samples, has shown an average decrease in the vertical coefficient of permeability of 83%, from 1.15 × 10-7 m/s for the untreated control samples, to 1.92 × 10-8 m/s in treated samples.

Physical-mechanical properties of microbially induced calcite precipitation-treated loess and treatment mechanism

Loess disintegration can lead to geotechnical engineering problems,e.g.,slope erosion,wetting-induced landslide,and hydroconsolidation.Microbially induced calcite precipitation(MICP)technique is a potential loess reinforcing method.This study investigated the physical-mechanical properties of MICP-treated loess and then explored the mechanism of loess modification by MICP.Here,loess first underwent MICP treatment,i.e.,mixing loess with Sporosarcina pasteurii and cementation solution(CS).Then,the effects of the CS concentration(0.2,0.6,0.8,and 1 M)on the physical and mechanical properties of the MICP-treated loess were tested.Finally,the static contact angle test,scanning electron microscopy(SEM),and X-ray diffractometry(XRD)were conducted to study the mechanism of MICP treatment on loess.Results showed the following property changes of loess after MICP treatment:the liquid limit decreased by 1.7%,the average particle size increased from 6 to 47μm,the specific gravity decreased from 2.65 to 2.43,the unconfined compressive strength increased from 37 to 71 k Pa,and the disintegration time increased from 10 to 25 min.Besides,the shear strength also increased,and the shear strength parameters(cohesion c and internal friction angle?)varied with the CS concentration.The static contact angle tests indicated that the water absorption ability of loess was reduced after MICP treatment.SEM and XRD results verified that the CaCO_(3)from MICP was attributed to the above results.The above findings explained the mechanism of MICP treatment of loess:the CaCO_(3)coats and cements the particles,and fills the pores of loess,improving the strength and water stability of loess.

Experimental study on mitigating wind erosion of calcareous desert sand using spray method for microbially induced calcium carbonate precipitation

Wind erosion is one of the significant natural calamities worldwide, which degrades around one-third of global land. The eroded and suspended soil particles in the environment may cause health hazards, i.e.allergies and respiratory diseases, due to the presence of harmful contaminants, bacteria, and pollens.The present study evaluates the feasibility of microbially induced calcium carbonate precipitation(MICP)technique to mitigate wind-induced erosion of calcareous desert sand(Thar desert of Rajasthan province in India). The temperature during biotreatment was kept at 36℃ to stimulate the average temperature of the Thar desert. The spray method was used for bioaugmentation of Sporosarcina(S.) pasteurii and further treatment using chemical solutions. The chemical solution of 0.25 pore volume was sprayed continuously up to 5 d, 10 d, 15 d, and 20 d, using two different concentration ratios of urea and calcium chloride dihydrate viz 2:1 and 1:1. The biotreated samples were subjected to erosion testing(in the wind tunnel) at different wind speeds of 10 m/s, 20 m/s, and 30 m/s. The unconfined compressive strength of the biocemented crust was measured using a pocket penetrometer. The variation in calcite precipitation and microstructure(including the presence of crystalline minerals) of untreated as well as biotreated sand samples were determined through calcimeter, scanning electron microscope(SEM), and energydispersive X-ray spectroscope(EDX). The results demonstrated that the erosion of untreated sand increases with an increase in wind speeds. When compared to untreated sand, a lower erosion was observed in all biocemented sand samples, irrespective of treatment condition and wind speed. It was observed that the sample treated with 1:1 cementation solution for up to 5 d, was found to effectively resist erosion at a wind speed of 10 m/s. Moreover, a significant erosion resistance was ascertained in15 d and 20 d treated samples at higher wind speeds. The calcite content percentage, thickness of crust,bulk density, and surface strength of biocemented sand were enhanced with the increase in treatment duration. The 1:1 concentration ratio of cementation solution was found effective in improving crust thickness and surface strength as compared to 2:1 concentration ratio of cementation solution. The calcite crystals formation was observed in SEM analysis and calcium peaks were observed in EDX analysis for biotreated sand.

Application of microbially induced carbonate precipitation to form biocemented artificial sandstone

It is difficult to collect and characterise well-preserved samples of weakly-cemented granular rocks as conventional sampling techniques often result in destruction of the cementation.An alternative approach is to prepare synthetic geomaterials to match required specifications.This paper introduces microbially induced carbonate precipitation(MICP)as a method to reliably deliver artificiallycemented specimens with customised properties,closely resembling those of soft carbonate sandstones.The specimens are generated from materials with two highly different particle size distributions(PSDs)to access a range of achievable combinations of strengths and porosities.The MICP parameters are kept constant across all samples to obtain similar calcium carbonate characteristics(size of individual crystals,type,etc.),while injected volume is varied to achieve different cementation levels.Although uniform cementation of very coarse sands has been considered very difficult to achieve,the results show that both the fine and coarse sand specimens present high degrees of uniformity and a good degree of repeatability.The unconfined compressive strengths(UCSs)(less than 3000 kPa)and porosities(0.25e0.4)of the artificial specimens fall in the same range of values reported for natural rocks.The strength gainwas greater in the fine sand than that in the coarse sand,as the void size in the latter was significantly larger compared to the calcium carbonate crystals’size,resulting in precipitation on less effective locations,away from contacts between particles.The strengths and porosities obtained for the two sands in this work fall within ranges reported in the literature for natural soft rocks,demonstrating theMICP technique is able to achieve realistic properties and may be used to produce a full range of properties by varying the grain sizes,and possibly the width of PSD.

MICP增强改性煤矸石在水稳材料中应用的试验研究

为解决煤矸石集料强度低、吸水率高、易崩解等问题,采用微生物诱导碳酸盐沉积(MICP)技术对煤矸石进行了增强改性。通过表观密度、吸水率、压碎值和超声波质量损失率的测试,同时结合SEM,EDS和XRD微观表征,研究了微生物矿化时间、菌液浓度和煤矸石粒径对MICP增强改性煤矸石性能的影响,并揭示了MICP增改性煤矸石的机理。将MICP增强改性煤矸石应用于水稳材料,通过无侧限抗压强度、间接抗拉强度和抗压回弹模量的测试,对比了MICP增强改性煤矸石水稳材料与普通煤矸石水稳材料的性能。结果表明:采用MICP增强改性技术可以提升煤矸石的物理力学性能,并且煤矸石的粒径越大增强改性效果越明显;在菌液OD600值(溶液在600 nm波长处的吸光值)为0.8、矿化改性7 d的条件下,MICP增强改性煤矸石比普通煤矸石的表观密度增加了14.66%,吸水率降低了40.94%,压碎值降低了7.93%;经MICP增强改性后的煤矸石表面包裹的生物CaCO_(3)方解石使得煤矸石的表观密度增加,吸水率和压碎值降低,强度提高,从而提升了煤矸石的性能;水泥稳定MICP增强改性煤矸石混合料最佳含水量比普通煤矸石水稳材料降低了17.3%,最大干密度增加了7.9%;MICP增强改性煤矸石水稳材料各龄期的无侧限抗压强度、间接抗拉强度和抗压回弹模量比普通煤矸石水稳材料均显著提升,表现出更高的强度、更好的抗裂性能和抗变形能力。

MICP与MgO联合加固粉土试验

微生物诱导碳酸钙沉积(MICP)技术利用特定微生物分解尿素产生碳酸根离子,与钙离子结合沉积生成碳酸钙,可对土体进行胶结加固。相比传统的化学加固,MICP具有环境友好、使用灵活等优点,但也面临处理步骤较多、加固效果不够稳定等问题。提出将活性MgO与MICP相结合,利用MICP反应提供氧化镁碳化所需的CO_(2),进一步提升加固效果。溶液试验表明,加入MgO会使溶液pH有所增加,使尿素水解速率降低;用MgO替代CaCl_(2)时的碳酸盐生成量低于使用CaCl_(2)时的生成量。粉土的加固试验结果表明,在粉土中掺入MgO然后进行MICP注浆处理,可有效降低试样崩解率并提高无侧限抗压强度,且掺入高活性MgO的效果更好。当MgO掺量在5%~20%时,试样加固强度与MgO掺量成线性正相关关系。相比仅使用MICP进行处理或仅在粉土中拌入MgO,MgO与MICP联合加固的强度更高,需要的处理次数更少。微观测试结果表明,MgO与MICP联合加固的试样中生成大量花瓣状或片状碱式碳酸镁,广泛分布在颗粒间和颗粒表面,起到了更强的胶结作用。

MICP加固花岗岩残积土的渗透特性

MICP技术可以显著降低固化土壤的渗透系数,然而目前没有关于MICP固化土壤渗透系数的理论计算方法。基于理论推导和试验验证的方法,研究MICP加固花岗岩残积土的渗透特性,提出MICP加固花岗岩残积土的碳酸钙生成量和渗透系数理论表达式。假设MICP的反应速率线性衰减,通过酶促反应动力学方程得到MICP加固土体的CaCO3生成量,估算CaCO3晶体的粒径和个数,从而获得加固后试样的孔隙比、迂曲度和颗粒比表面积,代入修正的Kozeny-Carman方程,得到加固后土体的渗透系数理论表达式。与试验数据对比分析结果表明:CaCO3的产量早期增加快,后期增加变缓并逐渐趋于稳定;MICP加固土体的渗透系数其具有早期降低快,后期趋于平稳的特征。胶结液浓度为0.50、0.75、1.00、1.25 kmol/m3的试样渗透系数最终分别降低了35%、40%、45%和55%。提出的CaCO3含量表达式和渗透系数表达式与试验结果拟合良好,可为微生物加固的设计计算提供参考。

基于高密度电阻率成像技术的MICP浆液入渗过程监测研究

微生物诱导碳酸钙沉淀(MICP)技术是一种生态环保、前景广阔的土体改性方法,其改性效果与浆液的入渗特征密切相关。为此,提出将高密度电阻率成像(ERT)技术用于MICP浆液入渗过程监测。文章通过开展模型试验,对石英砂试样进行混合一步注浆法MICP处理,同时对试样持续进行ERT监测及电导率分析,获取了试样的三维电阻率变化特征,处理完成后测定了试样中碳酸钙含量的空间分布。结果表明:(1)MICP反应过程中,砂土与注浆液电导率随尿素分解而逐渐升高;(2)注浆液的迁移分布对砂土内部低电阻区的分布规律起主导作用,而碳酸钙沉淀的影响较小;(3)在MICP处理过程中,碳酸钙沉淀的生成与注浆液的迁移渗透相互作用,共同影响改性效果;(4)ERT技术可有效监测MICP处理区电阻率的时空演化特征,准确反映注浆液渗透迁移情况,进而评价改性效果。研究结果表明,采用ERT技术监测MICP改性土体过程具有可行性,为评价和优化微生物矿化改性效果提供了新的技术思路和方向。

冻融循环作用下MICP固化铅污染土的强度与浸出特性研究

微生物诱导碳酸钙沉淀(MICP)技术可用于重金属污染土固化稳定修复。本文通过开展无侧限抗压强度、离子浸出及微观试验,主要研究MICP固化铅污染土在冻融循环作用下的强度与化学稳定性,并揭示其微观作用机理。结果表明:随着铅离子浓度的增加,土体的无侧限抗压强度先增大后减小,铅离子浸出浓度增大;随冻融循环次数的增加,土体的强度逐渐降低并趋于稳定,铅离子浸出浓度增大。冻融循环作用后,固化土的主要矿物成分未发生变化;土中的小孔隙数量增加,大孔隙数量基本保持不变。冻融循环作用损伤固化土的碳酸钙胶结与铅离子沉淀结构,致使土体性能劣化。

天然海水环境下离子浓度对MICP反应的影响

微生物岩土技术通过生物矿化过程改善基础材料的力学性质,使其更适用于建筑或解决多学科领域的环境问题。微生物矿化过程中产生的碳酸钙是改善基础材料力学性质的主要成分,但其生成量及形态等受多种因素的影响。通过离子计、pH计、SEM、EDS和XRD等手段探究天然海水和去离子水环境在矿化过程中氯化钙和尿素浓度、比例及菌液和胶结液(氯化钙、尿素)体积比等因素对沉淀物质形貌及晶体组成的影响。结果表明:钙离子和尿素浓度及比例低时,碳酸钙的产率较高,但当初始钙离子、尿素浓度超过1.0 mol/L时,离子浓度增大对细菌产脲酶有抑制作用,浓度越高对脲酶的抑制作用越明显,沉淀物产率也随之减小,海水环境总体沉淀量与沉淀效率均高于去离子水环境。菌胶结液体积比去离子水中为1∶4、海水中不高于1∶10时,碳酸钙生成量较高,去离子水环境晶型以方解石为主,海水环境晶型以球霰石为主且沉淀中含有镁盐。

MICP技术在地下水封油库渗控注浆中的应用潜力

地下水封油库在建设及运营过程中洞室涌水量大小是影响洞库水封安全和运营成本的重要因素。目前地下水封油库工程建设中采用传统的注浆方式难以将围岩渗透性降低到设计要求,因此洞室涌水量得不到很好的控制。微生物诱导碳酸钙沉淀(MICP)技术具有注浆黏度低、环境适应性强、生成矿化物质稳定等显著优点,引起了学术界与工程界广泛的兴趣和研究。本文首先分析了地下水封油库涌水量控制中存在的相关问题,然后阐述了MICP技术对裂隙渗流控制的机理、影响因素以及对裂隙渗透性的影响效果,最后探讨了MICP技术在地下水封油库中应用的关键问题。通过分析表明,MICP作为地下水封油库渗流控制的一种辅助注浆方式,可以较为准确地控制围岩渗透性变化,达到对洞室涌水量有效控制的目的。

椰壳纤维-MICP复合改良膨胀土膨胀特性研究

采用椰壳纤维联合微生物诱导碳酸钙沉积(MICP)技术对南水北调中线工程南阳段的膨胀土进行试验改良,对素土、纤维土、MICP土以及椰壳纤维-MICP复合改良土开展无荷膨胀率试验和有荷膨胀率试验,研究改良前后膨胀土无荷膨胀率、有荷膨胀率随纤维掺量的变化规律,并对比分析单一改良方式和复合改良方式下纤维掺量对膨胀土膨胀特性的影响,最后通过电镜扫描试验,观察土样微观结构,揭示纤维-MICP复合改良膨胀土特性的内在机理。结果表明:单掺椰壳纤维和MICP技术改良均可抑制膨胀土的膨胀性能,而椰壳纤维-MICP复合改良土的改良效果最明显,且随着纤维掺量的增加,纤维土和复合改良土的无荷膨胀率和有荷膨胀率呈现出先减后增的趋势,纤维最佳掺量为0.5%,电镜扫描试验显示椰壳纤维可发挥桥联的作用以增强MICP膨胀土的改良效果。

Fracture sealing based on microbially induced carbonate precipitation and its engineering applications:A review

In this review,the development and application of microbially induced carbonate precipitation(MICP)technology for the sealing of underground engineering fractures are discussed in detail.The importance of sealing micro-fractures in an environmentally friendly and efficient manner is emphasized,and the potential of the MICP method in controlling pore and fracture seepage is highlighted.The fundamental mechanisms,key influencing factors,numerical models,and applications of the MICP in the fields of geological CO_(2) storage and oil resources development are comprehensively summarized in the paper.At the same time,the limitations of the existing research and the future research directions are discussed,especially in terms of improving the processing efficiency,environmental impacts,and cost considerations.Overall,the development of MICP technology provides a new environmentally friendly reinforcement method for geotechnical engineering and is expected to play a key role in the future development of underground space engineering.

MICP技术联合多孔硅吸附材料对锌铅复合污染土固化/稳定化修复的试验研究

近年来,工业和科技的快速发展使得重金属污染土固化/稳定化的修复研究成为热点。运用微生物诱导碳酸钙沉淀(MICP)技术联合吸附材料对锌铅复合重金属污染土进行固化/稳定化的修复,通过无侧限抗压强度试验、毒性浸出试验,评价处理前后污染土的固化效果与重金属的稳定化效果,结合扫描电镜(SEM)和X射线衍射(XRD)等检测手段,揭示MICP技术处理锌铅重金属污染土的修复机制。研究结果表明,采用MICP技术对锌铅重金属污染土进行固化/稳定化之后,可以有效降低污染土中有害重金属的浸出性。当矿化时间为10d时,试样无侧限抗压强度为942.5k Pa;铅的浸出浓度为4.20mg/L,比未处理时降低了44.81%;锌的浸出浓度为4.31mg/L,比未处理时降低了46.19%,效果显著。在此基础上,添加10%的多孔硅吸附材料后,试样无侧限抗压强度可达到1 021 kPa,强度提高了8.3%;铅的浸出浓度为2.45mg/L,与未经处理时相比,降幅达到了67.81%,与单纯MICP方法处理时相比,铅浸出浓度被二次降低了41.67%;锌的浸出浓度仅为2.93 mg/L,与未经处理时相比,降幅达到了63.4%,与单纯MICP方法处理时相比,浸出浓度被二次降低了31.9%。多孔硅吸附材料的添加明显提升了MICP技术对锌铅复合重金属污染土的修复效果,由于多孔硅吸附材料对重金属离子的固定与吸附,污染土中重金属的浸出浓度减小,同时,吸附材料还可以作为碳酸钙晶体沉积的核位点,加速矿化反应。该研究提出了处理重金属污染土的新技术并揭示了其修复机制,为MICP技术联合多孔硅吸附材料对现场锌铅复合重金属污染土的修复与应用提供了理论与试验依据。

非饱和砂质黏性紫色土崩解特性及MICP加固试验

砂质黏性紫色土遇水极易崩解是导致西南山区土壤侵蚀流失等水土灾害的重要原因,为揭示其崩解规律和机制,改善土体的崩解性,采用自制崩解测量仪对不同初始干密度、含水率及颗粒级配条件下的紫色土进行浸水崩解试验,并从非饱和有效应力角度分析了其崩解演化机制,在此基础上,通过扫描电镜(Scanning Electron Microscope,SEM)探讨利用微生物诱导碳酸钙沉积(Microbial Induced Calcite Precipitation,MICP)加固技术对紫色土崩解性的改善效果。结果表明:1)紫色土浸水崩解全过程包含排气吸水期、平衡期、崩解发展期、崩解残余期4个阶段;2)崩解率与平均崩解速率随初始干密度及含水率的增大而减小,且细颗粒含量越高,平均崩解速率越大;3)紫色土浸水后非饱和有效应力的衰减过程受初始饱和度的影响较大,平均崩解速率随初始饱和度的增大呈指数函数衰减;4)MICP加固土的崩解率和平均崩解速率相较于素土分别下降了73~97个百分点和84%~99%,固化沉积的碳酸钙晶体使土体结构中的微裂隙与大孔隙大幅减少,形成较为致密的孔隙结构,大幅增强了粒间胶结强度,使土体抗崩解性能明显提升。MICP技术可以作为西南山区紫色土水土灾害防治的有效措施。

MICP固化粉土细菌的分布和固定规律研究

采用一维注浆方式对50 cm长柱状粉土试样进行微生物固化试验,通过测定孔隙液中细菌数量、NH+4浓度和pH、及固化土体中的胶结CaCO_3生成量等参量,分析注浆菌液配比和胶结液浓度对细菌与反应产物沿程分布特性的影响。结果表明,当注入浓度为1.223×108 CFU/mL的原菌液时,固定菌与游离菌沿柱状试样渗流方向沿程衰减显著,细菌主要分布于注浆端25 cm以内,提高胶结液浓度对试样碳酸钙生成量的影响主要集中在注浆端5 cm以内区域。当注入用营养液稀释的菌液(浓度8.20×106 CFU/mL)或用营养液稀释的上清液(浓度1.80×106 CFU/mL)时,孔隙液中细菌能快速繁殖增长且分布较为均匀,吸附菌和被拦截的游离菌共同组成固定菌,对土中碳酸钙的生成量产生影响,胶结液浓度的变化对碳酸钙生成量的影响较小。研究结果表明,微生物注浆加固粉土的均匀性主要受固定菌分布的均匀性控制,将菌液或上清液稀释后注入粉土能够使固定菌沿程分布均匀,可较好地改善固化土体均匀性。

MICP矿化产物中钙离子利用率的影响因素及微观物相分析

钙离子利用率是微生物诱导碳酸钙沉积矿化技术中一项重要指标和参数,待矿化钙离子能否参与到矿化反应和如何被利用是这项技术的关键。本文借助紫外线吸光度法、电导率法和EDTA滴定法等技术手段,分析了待胶结菌液浓度和脲酶活性的时变规律,阐述了不同胶结配比对矿化反应过程中钙离子利用率的影响。结果表明:在胶结过程中,细菌的浓度和脲酶活性会逐渐降低;在合理浓度范围内,钙离子利用率随菌液浓度以及胶结液浓度的增大而提高,最高可达99.73%。进而通过X射线衍射、扫描电镜检测来揭示矿化产物的形成机理,分析得出:球霰状碳酸钙晶体是钙离子在有机质的调控下依托细菌表面的成核位点富集矿化而成,矿化产物中碳酸钙晶体尺寸大小和形态受菌液和胶结液配比浓度的影响。本研究对于微生物诱导矿化反应生成碳酸钙在工程材料领域的应用具有一定的参考价值。

砂土基MICP土工材料剪切强度试验及可靠性分析

选用巴氏芽孢杆菌,以不同粒径砂土为岩土基质,应用微生物诱导矿化技术生成MICP-土工材料试样,自然养护7d后,应用直剪仪进行了抗剪强度测试试验。结果表明,MICP-细砂土内摩擦角范围最大,MICP-粗粒砂土内摩擦角范围最小,这与微生物诱导生成的矿化物填充空隙的过程中形成胶结作用有重要的关系,粗粒砂土空隙大,MICP材料强度的增长主要依靠诱导生成的碳酸钙咬合力;中粗砂粒土表面粗糙度的提高有效增强了矿化土工材料的强度;细砂土主要是填充空隙,材料更加密实,导致抗剪强度最大。再运用多项式混沌扩展(PCE)方法建立代理模型,求得其前四阶统计矩,对内摩擦角输出响应的不确定性进行了量化。