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走滑断层作用下上覆土层的变形破坏机理

裴鹏程, 黄帅, 袁静, 张智康

裴鹏程,黄帅,袁静,等. 走滑断层作用下上覆土层的变形破坏机理[J]. 中国地质灾害与防治学报,2024,35(6): 115-127. DOI: 10.16031/j.cnki.issn.1003-8035.202306029
引用本文: 裴鹏程,黄帅,袁静,等. 走滑断层作用下上覆土层的变形破坏机理[J]. 中国地质灾害与防治学报,2024,35(6): 115-127. DOI: 10.16031/j.cnki.issn.1003-8035.202306029
PEI Pengcheng,HUANG Shuai,YUAN Jing,et al. Deformation and failure mechanism of overlying soil lavers under strike-slip fault action[J]. The Chinese Journal of Geological Hazard and Control,2024,35(6): 115-127. DOI: 10.16031/j.cnki.issn.1003-8035.202306029
Citation: PEI Pengcheng,HUANG Shuai,YUAN Jing,et al. Deformation and failure mechanism of overlying soil lavers under strike-slip fault action[J]. The Chinese Journal of Geological Hazard and Control,2024,35(6): 115-127. DOI: 10.16031/j.cnki.issn.1003-8035.202306029

走滑断层作用下上覆土层的变形破坏机理

基金项目: 国家重点研发计划项目(2022YFC3070103-01);地震数值预测联合实验室开放基金(2021LNEF04); 博士后基金项目(2021M691391)
详细信息
    作者简介:

    裴鹏程(1998—),男,重庆垫江人,土木工程专业,硕士研究生,主要从事管土交互耦合作用研究。E-mail:pengcheng-pei@foxmail.com

    通讯作者:

    黄 帅(1987—),男,山东肥城人,土木工程专业,博士,研究员,主要从事流域重大工程抗震分析与韧性提升研究。E-mail:huangshuai3395@163.com

  • 中图分类号: P642.21

Deformation and failure mechanism of overlying soil lavers under strike-slip fault action

  • 摘要:

    随着西部大开发的推进,工程项目难免需要跨越断裂带。断裂带具有地震活动频繁、岩层错动等特点,这给工程建设和资源开发带来了不小的挑战。为探明跨断层工程结构的敏感性影响因素,文章研究了不同基岩位错量、不同基岩错动速率、跨越断层角度、不同场地土类型和不同场地土厚度对上覆土层的变形破坏和竖向应力的影响机制。结果表明:基岩位错会导致覆土层产生应力集中、破裂、滑动等破坏现象,这些破坏可能会引起土体位移,从而引发山体滑坡、地滑和地面变形等地质灾害的问题,将提高对地下管道、道路、桥梁等工程设施造成损伤破坏的风险。文章聚焦基岩位错造成地面沉降变形、塌陷等问题,发现随着基岩位错量的增大,不同场地土对覆土层的沉降位移、竖向应力都有不同幅度的增长,例如坚硬土基岩位错量2 m时比0.4 m时沉降变形和竖向应力增长5倍左右。此外,发现在跨越断层时选择以90°跨越断层,可以减小沉降变形和应力。相关研究旨在揭示上覆土层的变形破坏以期对不可避免的跨断层工程结构的变形以及抗剪切破坏加固提供技术支撑。

    Abstract:

    With the advancement of the western development, engineering projects inevitably need to traverse fault zones. However, fault zones are typically characterized by frequent seismic activities and rock layer dislocations, which bring certain challenges to both construction and resource development. To explore the sensitivity factors affecting the sensitivity of cross-fault engineering structures, this study investigates the effects of different bedrock dislocation amouts, bedrock dislocation rates, fault-crossing angles, different types of soil at the site, and varying soil thicknesses on the deformation, failure, and vertical stress mechanisms of overlying soil layers. The results show that bedrock dislocation can lead to stress concentration, fractures, sliding, and other destructive phenomena in overlying soil layers. These damages may cause soil displacement, potentially triggering geological hazards such as landslides, ground slides, and ground deformations. This poses a high risk of damage and destruction of the underground pipelines, roads, bridges, and other engineering facilities. This paper focuses on issues such as ground settlement deformation and collapse caused by rock dislocation, revealing that with an increase in rock dislocation amount, different types of soil at the site exhibit varying degrees of increase in settlement displacement and vertical stress on the overlying soil layer. For example, with the bedrock dislocation amount of 2 m compared to 0.4 m in hard soil, settlement deformation and vertical stress increase by around five times. In addition, it was found that selecting a 90° angle for fault crossing can reduce settlement deformations and stresses. The study aims to reveal the deformation damage of the overlying soil layer, providing technical support for the inevitable deformation of cross-fault engineering structures as well as the reinforcement against shear damage.

  • 膨胀土边坡的稳定性一直是岩土界广泛关注的问题。目前,边坡稳定性分析的常用方法主要包括了极限平衡法、极限分析法等,都建立在极限平衡理论基础之上,并不适用于膨胀土边坡的稳定性分析[1]。另一种常用的方法是有限元强度折减法,早在1975年该方法就被Zienkiewice等[2]用来求解边坡稳定问题,随着计算机硬件技术和有限元软件技术的飞速发展,运用有限元强度折减法分析边坡稳定已经成为新的趋势[3-10]。国内很多学者将强度折减法运用到膨胀土边坡稳定分析中,取得了一系列成果。

    周健等[11]利用强度折减法研究膨胀土边坡的稳定性,发现干湿循环会导致膨胀土抗剪强度衰减,且随着干湿循环次数的增加,边坡稳定性降低,安全系数减小。刘明维等[12]研究了强度折减法在膨胀土斜坡地基路堤稳定性分析中的应用,发现强度折减法所得结果与实际情况相符。张硕等[3]基于有限元强度折减法研究了雨季土体增重、强度降低和膨胀作用对膨胀土边坡稳定性的影响,发现强度降低是导致边坡失稳的主要原因,膨胀作用次之,土体增重较小。程灿宇等[13]利用MIDAS/GTS、FLAC和ANSYS三种软件采用强度折减法分别对不同工况进行了稳定性分析,发现弱膨胀土边坡无论采用M-C屈服准则,还是D-P屈服准则所得结果差异不大。谭波等[14]采用强度折减法对不同条件下的膨胀土边坡的安全系数进行了计算,发现次生裂隙面发育是导致膨胀土边坡失稳的主要原因之一。杨才等[15]根据强度折减有限元法对不同条件失稳边坡稳定性分析结果,提出以最大塑性应变以及最小塑性应变的量级指标来判定塑性区贯通时刻。

    然而,干湿循环、降雨入渗等因素会引起浅层膨胀土干密度降低、吸力衰减,从而使抗剪强度大幅度下降。目前,在采用强度折减法分析膨胀土边坡稳定性的同时系统考虑抗剪强度衰减影响的研究尚不多见。为此,本文采用试验与数值模拟相结合的方式,系统地考虑了抗剪强度衰减特性的膨胀土边坡稳定性分析。首先对广西宁明膨胀土开展了室内直剪试验,分析了含水量、干密度对膨胀土抗剪强度衰减的影响;再以此为依据,利用Midas有限元分析软件研究考虑抗剪强度衰减特性对膨胀土边坡稳定性安全系数的影响,获取了边坡安全系数随抗剪强度折减的动态变化规律,以期为工程实践提供参考。

    土样取自广西崇左-夏石镇某高速公路膨胀土边坡路段,其天然含水量、最优含水量和天然干密度分别为32.5%,24%和1.40 g/cm3,其他土性指标,比重(Gs),液限(WL),塑限(WP),塑性指数(IP),自由膨胀率(σf)见表1。自由膨胀率为42.8%,按照《膨胀土地区建筑技术规范》[16]的分类,该膨胀土为弱膨胀性膨胀土。

    表  1  宁明膨胀土基本土体参数
    Table  1.  Basic soil parameters of Ningming expansive soil
    参数Gs/(g.cm−3wL/%wP/%IPσf/%
    取值2.8059.1124.6834.4342.8
    下载: 导出CSV 
    | 显示表格

    首先,将现场取回的扰动土试样碾散过2 mm筛,过筛后放入105℃的烘箱中烘24h,使试样具有相同的初始结构,并将烘干土用收纳箱密封保存备用。接着,按目标含水量(控制干密度为1.6 g/cm3)和目标干密度(控制含水量18%)要求配制成湿土,并装入保鲜袋,经闷料24 h后测得土样的最终含水量与目标含水量之间误差不超过1%;最后,为保证环刀试样均匀一致,采用自制的模具(图1)进行制样,并利用液压千斤顶脱模推出,控制试样的直径为61.8 mm,高度为15 mm,目的是使试样在竖直方向上能够充分膨胀,每组平行土样密度差不超过±0.02 g/cm3,否则废弃重做。试样配制过程如图2,最终制成的每个环刀试样表面均平整无破损,且长度误差不超过0.2 mm,则为满足要求的试样。

    图  1  制样模具
    Figure  1.  Sample preparation mould
    图  2  配土过程示意图
    Figure  2.  Diagram of the soil preparation process

    以初始干密度为1.6 g/cm3,含水量分别为9%、12%、15%、18%、21%、24%和27%制取环刀试样7组,每组4个;并以初始含水量为18%,干密度分别为1.4、1.5、1.6和1.7 g/cm3制取环刀试样4组,每组4个,然后进行常规直剪试验(图3),试验施加的竖向压力分别为100 kPa、200 kPa、300 kPa、400 kPa,剪切速率为0.02 mm/min,初始剪切位移均保持在3.850 mm左右,剪切位移量程13.000 mm。

    图  3  四联直剪仪
    Figure  3.  Quadruple direct shear testing device

    为研究广西宁明膨胀土的抗剪强度随含水量变化的规律,对不同含水量的土样进行直剪试验,试验结果如表2所示。

    表  2  宁明膨胀土抗剪强度试验结果表
    Table  2.  Results of shear strength of Ningming expensive soils
    试验参数w/%φ/(°)c/kPa
    试验结果8.8027.3100.36
    11.724.5693.28
    14.621.8067.34
    17.519.8254.64
    20.817.9241.22
    23.315.2030.86
    26.112.389.90
    下载: 导出CSV 
    | 显示表格

    根据表2可绘制出宁明膨胀土黏聚力和内摩擦角与含水量的关系如图4图5所示,拟合后可得到黏聚力和内摩擦角与含水量的关系式:

    图  4  宁明膨胀土黏聚力随含水量变化规律
    Figure  4.  Variation of cohesive force of Ningming expansive soil with water content
    图  5  宁明膨胀土内摩擦角随含水量变化规律
    Figure  5.  Variation of internal friction angle of Ningming expansive soil with water content
    $$ c = { - 5.192}w + 147.9 $$ (1)
    $$ \varphi = - 0.827w + 34.36 $$ (2)

    由式(1)和(2)可知,cφw都存在近似线性的关系,这与文献[17-18]结果一致,含水量每增大5%,其黏聚力约减小26 kPa,内摩擦角减小4.2°左右;为更好的表示cw的衰减规律,参考吕海波等[19]的研究,可计算出c的衰减率为:

    $$ \eta = \frac{{\left| {{c_0} - {c_1}} \right|}}{{{c_0}}} \times 100\% $$ (3)

    式中:η——黏聚力衰减率;

    c0——初始黏聚力;

    c1——随含水量变化后的黏聚力。

    根据表3可知,随着宁明膨胀土含水量的逐渐增大黏聚力不断衰减,在最低目标含水量9%以3%递增至目标含水量27%的过程中,黏聚力的衰减率变化趋势为增大-减小-增大,说明膨胀土在低含水量和接近饱和含水量时,黏聚力对含水量的变化显得十分敏感。

    表  3  宁明膨胀土黏聚力衰减率计算结果表
    Table  3.  Results of cohesion decay rate of Ningming expansive soil
    试验参数w/%c/kPaη/%
    试验结果8.8100.36
    11.793.287.05
    14.667.3427.81
    17.554.6418.86
    20.841.2224.56
    23.330.8625.13
    26.19.967.92
    下载: 导出CSV 
    | 显示表格

    在试样ρd保持一致的情况下(1.6 g/cm3),可从图6图7中看出在相同垂直应力作用下,抗剪强度随着w的增大呈现减小的趋势。

    图  6  不同含水量试样抗剪强度随垂直压力的变化
    Figure  6.  Change of the shear strength with vertical pressure of samples with different water contents
    图  7  不同荷载下试样抗剪强度随含水量的变化
    Figure  7.  Change of the shear strength with water content of specimens undergoing different vertical loads

    上述试验结果表明,宁明膨胀土的抗剪强度随着含水量的改变发生显著变化;主要表现为在含水量增大时黏聚力和内摩擦角发生衰减,其中黏聚力的衰减较内摩擦角更为明显。

    根据表4数据可拟合出试样黏聚力和内摩擦角随干密度的变化规律,如图8图9所示。

    表  4  不同干密度下试样试验结果记录表
    Table  4.  Record table of test results under different dry densities
    试验参数ρd/(g·cm−3c/(kPa)φ/(°)
    试验结果1.797.2626.5
    1.654.6419.82
    1.540.3417.82
    1.437.5716.87
    下载: 导出CSV 
    | 显示表格
    图  8  宁明膨胀土黏聚力随干密度变化规律
    Figure  8.  Variation of cohesive force of Ningming expansive soil with dry density
    图  9  宁明膨胀土内摩擦角随干密度变化规律
    Figure  9.  Variation of internal friction angle of Ningming expansive soil with dry density

    图8图9可观察出宁明膨胀土的黏聚力和内摩擦角随干密度的变化曲线符合乘幂函数的拟合结果,其中:

    $$ c = 0.126{{\rm{e}}^{3.884{\rho _{\rm{d}}}}} $$ (4)
    $$ \varphi = 1.631{{\rm{e}}^{1.614{\rho _{\rm{d}}}}} $$ (5)

    分析式(4)可知试样c随着ρd的减小而减小,且随着ρd的减小,c的衰减速率由快到慢,并最终趋于稳定;而在接近最大干密度(1.78 g/cm3)时变化较为显著,在干密度由1.4 g/cm3增大至1.6 g/cm3时,c增加了17.07 kPa;在干密度由1.6 g/cm3增大至1.7 g/cm3时,c增加了42.62 kPa。而由式(5)能看出φ亦随着ρd的减小而减小,但其整体的变化幅度并不大,干密度1.4 g/cm3与1.7 g/cm3的试样φ相差约9.6°;图10中各级载荷下的抗剪强度都随着试样ρd的减小而降低,且其变化幅度在高垂直应力条件下更为显著。

    图  10  不同干密度下试样抗剪强度随垂直应力的变化
    Figure  10.  Variation of shear strength with vertical stress of specimens of different dry densities

    干密度对宁明膨胀土抗剪强度的影响主要体现在黏聚力上,试样干密度越小,单位体积土体的土颗粒越少,土粒间水膜越薄,其抗剪强度越小;此外,膨胀土干密度越小,其吸力越大,试样的抗剪强度越低;而干密度对于内摩擦角的整体影响并不显著,其变化在10°以内。

    根据广西崇左-夏石镇某高速公路膨胀土边坡为研究对象,并参考该公路的地质勘察报告,该边坡土质主要由填土(①1和①2)、黏土②、强风化泥岩③和中风化泥岩④组成。同时根据地质调查及钻探、探槽揭示,该边坡滑动带基本位于黏土层,且下部强风化泥岩等土体不透水,大气影响深度为7 m,刚好大致为填土厚度和黏土厚度之和,影响急剧层深度为2.5 m。相关土层天然状态下基本参数指标见表5

    表  5  土层相关参数
    Table  5.  Soil layer related parameters
    地层岩性厚度
    /m
    重度
    /(kN·m−3
    内摩擦角
    /(°)
    黏聚力
    /kPa
    其它
    填土①10.2~118.0524成分黏土
    填土①22.5~3.318.8307上层砾砂,
    下层碎石
    黏土②0.3~418.48.435.6中等膨胀土
    强风化泥岩③0.6~119.32545质量等级Ⅴ级
    中风化泥岩④未钻穿19.63565质量等级Ⅴ级
    下载: 导出CSV 
    | 显示表格

    结合上述实际工程地质勘察报告,将膨胀土边坡考虑为非匀质边坡,同时为提高模型求解时间,取黏土弹性模量12000 kPa,容重18.4 N/m3,泊松比0.3,边坡高20 m,坡比1∶1.5。为避免尺寸效应带来的误差和便于模型求解收敛,坡顶取15 m,坡底取25 m,网格按线性梯度(长度)划分,起始长度1.2 m,结束长度0.5 m。由于填土土层由于土体较松散,易膨胀开裂,在降雨作用下容易引发降雨入渗,易软化下部土体,因此实际工程中对该部分填土进行了挖除。填土挖除后,为充分合理考虑到大气影响层对膨胀土边坡中黏土的影响,同时又不会影响到下部不透水泥岩,取大气影响层为距离坡面4 m范围的土体,正好为黏土厚度,急剧层为距离坡面1.5 m范围的土体(图11)。

    图  11  模型示意图
    Figure  11.  Numerical simulation model

    根据室内直剪试验结果,同时考虑到膨胀土具有浅层性,将测得的7个含水量下(干密度均为1.6 g/cm3)的膨胀土抗剪强度参数指标cφ赋予给受大气影响的风化层土体,即距离坡面4 m范围内的黏土。强、中风化泥岩层土体参数指标取地质勘察报告的值,具体数值见表5。计算得到不同含水量w下膨胀土边坡整体位移和潜在滑移面,如图12图13所示。

    图  12  1.6 g/cm3干密度不同含水量条件下的边坡位移
    Figure  12.  Slope displacement with the 1.6 g /cm3 dry density under different moisture content conditions
    图  13  1.6 g/cm3干密度不同含水量条件下的边坡潜在滑移面
    Figure  13.  Potential slip surface of slope with the dry density of 1.6 g/cm3under different moisture content

    分析图12图13可知,随着含水量w的增大,边坡的整体位移整体呈增大趋势,非饱和膨胀土边坡的浅层破坏由受大气影响层膨胀土强度衰减导致。随着含水量的增加,土体的c不断减小,边坡位移不断增大,滑移面逐渐变浅;破坏形式为浅层滑塌式的破坏。边坡失稳的滑移面位置位于大气影响层和不透水泥岩的交界处,且与黏土的底部相切。

    基于相同干密度,不同含水量下膨胀土的剪切试验和地质勘察报告,利用有限元分析软件对边坡进行稳定性分析,可得到随着膨胀土含水量的变化对边坡稳定性安全系数的影响规律,如图14所示的曲线,表达式为:

    图  14  边坡安全系数随含水量的变化规律
    Figure  14.  The variation of slope safety factor with water content
    $$ y = - {\text{0}}{\text{.008}}{x^2} + {\text{0}}{\text{.1884}}x + {\text{2}}{\text{.025}} $$ (6)

    随着w的增大,膨胀土的强度参数指标不断衰减,含水量较高比低含水量情况下的衰减速度更大。同时,膨胀土边坡在天然状况下处于稳定状态,但当w增大至27%时,其Fs为0.850,稳定性转变为失稳状态,发生滑坡、坍塌等工程现象;在此基础上,若继续增大含水量,膨胀土边坡将可能由浅层失稳进入完全失稳状态,这与实际工程中,在长时间降雨后,曾出现的多次滑坡现象类似。

    根据试验结果,将测得的四个干密度下(含水量均为18%)的膨胀土抗剪强度参数指标cφ赋予给距离坡面4 m范围的黏土。强、中风化泥岩层土体抗剪强度参数指标取地质勘察报告值,具体数值见表5。计算得到不同ρd下膨胀土边坡整体位移和潜在滑移面,如图15图16所示。

    图  15  18%含水量不同干密度条件下的边坡位移
    Figure  15.  Slope displacement under different dry densities with the moisture content of 18%
    图  16  18%含水量不同干密度条件下的边坡潜在滑移面
    Figure  16.  Potential slip surface of slope under different dry densities with the 18% moisture content

    图15图16中可以看出试样的ρd越小,边坡位移越大,潜在滑移面变浅;这是因为土体的c随着ρd的减小而减小,使得其抗剪强度降低;此时,边坡的破坏形式由整体滑动变为浅层滑塌。基于相同含水量,不同干密度下膨胀土的剪切试验和地质勘察报告,利用有限元分析软件对边坡进行稳定性分析,可得到随着膨胀土干密度的变化对边坡稳定性安全系数的影响规律,如图17所示的曲线,其表达式为:

    图  17  边坡安全系数随干密度的变化规律
    Figure  17.  The variation of slope safety factor with dry density
    $$ y = {\text{8}}{\text{.375}}{x^2} - {\text{23}}{\text{.24}}x + {\text{18}}{\text{.41}} $$ (7)

    试样ρd越小,其抗剪强度越低;且在ρd越大时其Fs增大趋势越为显著;1.5 g/cm3干密度下的Fs为2.409,比1.4 g/cm3的高出0.124,而1.7 g/cm3干密度下的Fs与1.6 g/cm3条件下的差值为0.459。

    (1)含水量的增大、干密度的减小都会引起膨胀土的峰值抗剪强度、黏聚力以及内摩擦角发生不同程度的衰减,其中,黏聚力的衰减幅度相较于内摩擦角更大。

    (2)通过多次膨胀土强度折减的方法可以很好地模拟降雨过程中由抗剪强度衰减引起的边坡稳定性的动态变化:风化层土体强度接近未风化层土体强度时,边坡处于稳定状态,潜在滑动面穿过分层界面;随着含水量增大、干密度变小,风化层抗剪强度会不断衰减,引起潜在滑动面逐渐外移,边坡稳定性降低。

    (3)数值模拟结果表明:与干密度减小相比,含水量的增大对边坡稳定更为不利,含水量增加到27%以后,膨胀土边坡由稳定状态变为欠稳定状态,因此在分析膨胀土边坡稳定性时,应着重考虑含水量变化的影响。

  • 图  1   鲜水河断裂带位置图

    Figure  1.   Location map of Xianshuihe fault zone

    图  2   有限元模型

    Figure  2.   Finite element model

    图  3   最大应力云图

    Figure  3.   Maximum stress contour map

    图  4   炉霍段沿迹线(X轴)的竖向应力

    Figure  4.   Vertical stress along the fault zone in the Luhuo section

    图  5   炉霍段沿断裂带方向(Z轴)的剪切位移

    Figure  5.   Shear stress along the fracture zone in the Luhuo section

    图  6   炉霍段沿迹线(X轴)的位移

    Figure  6.   Settlement displacement of the Luhuo section along the fault zone

    图  7   不同错动速率时的竖向应力

    Figure  7.   Vertical stress at different dislocation rates

    图  8   不同错动速率时的竖向位移

    Figure  8.   Settlement displacement at different dislocation rates

    图  9   不同角度跨越断层时的竖向应力

    Figure  9.   Vertical stress at different angles of fault crossing

    图  10   不同角度跨越断层时的竖向位移

    Figure  10.   Settlement displacement at different angles of fault crossing

    图  11   不同场地土的竖向应力

    Figure  11.   Vertical stress of soil in different sites

    图  12   不同场地土的竖向位移

    Figure  12.   Settlement displacement of soil in different sites

    图  13   覆土层30 m时不同场地土的竖向应力

    Figure  13.   Vertical stress of different site soils at a depth of 30 m

    表  1   土体参数

    Table  1   Soil parameters

    介质类型 密度/(kg·m−3 弹性模量/MPa 泊松比 黏聚力/kPa 摩擦角/(°)
    基岩 2750 60000 0.28 1200 40
    上覆土层 1850 110 0.32 10 37
    下载: 导出CSV

    表  2   土体参数

    Table  2   Summary of soil parameters

    土的类型 岩土名称和性状 密度
    /(kg·m−3
    弹性模量
    /MPa
    泊松比 黏聚力
    /kPa
    摩擦角
    /(°)
    实际剪切
    波速/(m·s−1
    土层剪切
    波速/(m·s−1
    坚硬土(岩石) 稳定的岩石,密实的碎石子 2250 1465 0.30 200 30 500 Vs≥500
    中硬土 中密、稍密的碎石子,密实、中密的砾、粗、中砂,
    fak>200的黏性土和粉土,坚硬黄土
    2050 650 0.31 100 20 350 500≥Vs>250
    中软土 稍密的砾、粗、中砂,除松散外的细、粉砂,
    fak<200的黏性土和粉土,fak≥130的填土,可塑黄土
    1850 110 0.32 10 37 150 250≥Vs>140
    软弱土 淤泥和淤泥质土,松散的砂,新近沉积的黏性土和
    粉土,fak<130的填土,新近堆积黄土和流塑黄土
    1700 45 0.35 10 25 100 Vs≤140
      注:fak为地基承载力特征值。
    下载: 导出CSV
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  • 期刊类型引用(5)

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出版历程
  • 收稿日期:  2023-06-20
  • 修回日期:  2023-10-09
  • 录用日期:  2023-12-19
  • 网络出版日期:  2024-03-24
  • 刊出日期:  2024-12-24

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