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Article(id=1322506490552894107, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506406058635943, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.10.498, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1730304000000, receivedDateStr=2024-10-31, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239718330, onlineDateStr=2026-10-29, pubDate=1763136000000, pubDateStr=2025-11-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239718330, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239718330, creator=13701087609, updateTime=1793239718330, updator=13701087609, issue=Issue{id=1322506406058635943, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='11', pageStart='1101', pageEnd='1210', issueExtLink='null', onlineDate='null', pubDate='1763136000000', pubDateStr='2025-11-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239698184, creator='13701087609', updateTime=1793239698184, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=1163, endPage=1170, ext={EN=ArticleExt(id=1322506491014267548, articleId=1322506490552894107, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Spatio-Temporal Deformation Characteristics of Landslides Based on Strain Analysis, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A two-dimensional strain tensor model is established to analyze the spatio-temporal deformation characteristics of a landslide. The results indicate that the landslide deformation exhibits spatio-temporal heterogeneity. During the initial monitoring stage, the front edge of landslide was dominated by compressive deformation, while the middle and rear edges showed a combination of expansion and shear deformation, with intensity rapidly decreasing over time. After the reinforcement of retaining wall, a brief period of strong compressive deformation occurred at the front edge of landslide, with a maximum compressive strain rate of -6 μstrain. In April 2021, a localized landslide occurred at the rear edge of landslide, characterized by strong localized tensile and shear deformation, with a maximum shear strain rate of 150 μstrain and a surface expansion strain peak of 30.9 μstrain. After the sliding event, only the surface expansion intensity diminished rapidly. Moreover, strain extremes along the crack between PB03 and PB04 persisted over time, showing a polarity reversal six months before the landslide, revealing potential risks even during the macroscopically stable deformation stage.

, authors=Zhanrong ZHU1, Xiaotao LI1, Xiaolong WU2, *, authorsList=Zhanrong ZHU, Xiaotao LI, Xiaolong WU, authorCompany=null, correspAuthors=Xiaolong WU, authorNote=

ZHU Zhanrong, senior engineer, majors in mine geological environment monitoring, E-mail:

, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322506494411653807, articleId=1322506490552894107, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=基于应变分析的滑坡时空变形特征研究, columnId=1322506197874356701, journalTitle=大地测量与地球动力学, columnName=地壳运动, runingTitle=null, highlight=null, articleAbstract=

建立二维应变张量模型定量分析某滑坡的时空变形特征。结果显示, 滑坡变形具有时空异质性。监测初期, 滑坡前缘以压缩变形为主, 中后缘膨胀与剪切变形共存, 强度随时间迅速衰减。挡土墙加固后, 滑坡前缘出现短时强挤压变形, 最大压应变率达-6 μstrain。2021-04滑坡后缘出现局部滑坡, 变形以局部强拉张和强剪切为主, 最大剪应变率为150 μstrain, 面膨胀极值为30.9 μstrain。滑动后, 仅面膨胀强度快速衰减。此外, 沿PB03和PB04之间裂缝的应变极值长期存在, 并在滑坡发生前半年出现正负转换现象, 揭示了滑坡宏观变形稳定阶段仍存在潜在风险。

, authors=朱占荣1, 李小涛1, 吴啸龙2, *, authorsList=朱占荣, 李小涛, 吴啸龙, authorCompany=null, correspAuthors=吴啸龙, authorNote=

朱占荣, 高级工程师, 主要研究方向为矿山地质环境监测, E-mail:

, correspAuthorsNote=

吴啸龙, 博士, 讲师, 主要研究方向为高危变形体动态变形监测与预警, E-mail:

WU Xiaolong, PhD, lecturer, majors in dynamic deformation monitoring and early warning of high-risk deformation bodies, E-mail:

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基于应变分析的滑坡时空变形特征研究
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朱占荣 1 , 李小涛 1 , 吴啸龙 2, *
大地测量与地球动力学 | 地壳运动 2025,45(11): 1163-1170
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大地测量与地球动力学 |地壳运动 2025 , 45 (11) : 1163 -1170
基于应变分析的滑坡时空变形特征研究
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朱占荣1 , 李小涛1, 吴啸龙2, *
作者信息
  • 1 陕西省一八五煤田地质有限公司, 陕西省榆林市人民西路283号, 719000
  • 2 西安科技大学测绘科学与技术学院, 西安市雁塔中路58号, 710054
通讯作者:

吴啸龙, 博士, 讲师, 主要研究方向为高危变形体动态变形监测与预警, E-mail:

WU Xiaolong, PhD, lecturer, majors in dynamic deformation monitoring and early warning of high-risk deformation bodies, E-mail:

作者简介:

朱占荣, 高级工程师, 主要研究方向为矿山地质环境监测, E-mail:

Spatio-Temporal Deformation Characteristics of Landslides Based on Strain Analysis
Zhanrong ZHU1 , Xiaotao LI1, Xiaolong WU2, *
Affiliations
  • 1 Shaanxi 185 Coal Field Geology Co Ltd, 283 West-Renmin Road, Yulin 719000, China
  • 2 College of Geomatics, Xi'an University of Science and Technology, 58 Mid-Yanta Road, Xi'an 710054, China

    • ZHU Zhanrong, senior engineer, majors in mine geological environment monitoring, E-mail:

出版时间: 2025-11-15 doi: 10.14075/j.jgg.2024.10.498
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摘要
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建立二维应变张量模型定量分析某滑坡的时空变形特征。结果显示, 滑坡变形具有时空异质性。监测初期, 滑坡前缘以压缩变形为主, 中后缘膨胀与剪切变形共存, 强度随时间迅速衰减。挡土墙加固后, 滑坡前缘出现短时强挤压变形, 最大压应变率达-6 μstrain。2021-04滑坡后缘出现局部滑坡, 变形以局部强拉张和强剪切为主, 最大剪应变率为150 μstrain, 面膨胀极值为30.9 μstrain。滑动后, 仅面膨胀强度快速衰减。此外, 沿PB03和PB04之间裂缝的应变极值长期存在, 并在滑坡发生前半年出现正负转换现象, 揭示了滑坡宏观变形稳定阶段仍存在潜在风险。

滑坡  /  时空变形  /  应变分析  /  面膨胀  /  最大剪应变

A two-dimensional strain tensor model is established to analyze the spatio-temporal deformation characteristics of a landslide. The results indicate that the landslide deformation exhibits spatio-temporal heterogeneity. During the initial monitoring stage, the front edge of landslide was dominated by compressive deformation, while the middle and rear edges showed a combination of expansion and shear deformation, with intensity rapidly decreasing over time. After the reinforcement of retaining wall, a brief period of strong compressive deformation occurred at the front edge of landslide, with a maximum compressive strain rate of -6 μstrain. In April 2021, a localized landslide occurred at the rear edge of landslide, characterized by strong localized tensile and shear deformation, with a maximum shear strain rate of 150 μstrain and a surface expansion strain peak of 30.9 μstrain. After the sliding event, only the surface expansion intensity diminished rapidly. Moreover, strain extremes along the crack between PB03 and PB04 persisted over time, showing a polarity reversal six months before the landslide, revealing potential risks even during the macroscopically stable deformation stage.

landslide  /  spatio-temporal deformation  /  strain analysis  /  surface expansion  /  maximum shear strain
朱占荣, 李小涛, 吴啸龙. 基于应变分析的滑坡时空变形特征研究. 大地测量与地球动力学, 2025 , 45 (11) : 1163 -1170 . DOI: 10.14075/j.jgg.2024.10.498
Zhanrong ZHU, Xiaotao LI, Xiaolong WU. Spatio-Temporal Deformation Characteristics of Landslides Based on Strain Analysis[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (11) : 1163 -1170 . DOI: 10.14075/j.jgg.2024.10.498
正文
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坡体变形的时空特征是揭示滑坡致灾机理和评估风险状态的重要依据[1]。大地测量技术因其大范围、高精度的技术优势，被广泛应用于滑坡灾害监测预警工作中。GNSS、InSAR和全站仪等监测技术可以在mm级精度上观测特定点的位置变化，常用于滑坡变形监测等相关研究[2-9]。但这些技术主要被用于离散点的位移量观测，包括位置变化时间序列分析，对于变形过程中的局部相关性和属性特征的定量分析不足。基于UAV(unmanned aerial vehicle)的摄影测量技术虽然实现了局部面状变形监测，但研究依然集中于位移场的空间分布，主要用于识别监测区域的最大位移位置和优势变形方向[10-12]。
现有的大地测量技术虽已在时间和空间精度上满足滑坡变形监测的需求，但多数研究主要致力于获取更高精度、更高分辨率的变形数据，对监测数据中蕴含的变形特征分析较为薄弱，缺少对变形属性特征的定量描述。为解决该问题，本文推导并建立基于小变形条件和有限变形条件下的应变模型，并以山西省某煤矿附近的一处复活古滑坡为例，通过应变分析量化研究该滑坡体在滑前演化、失稳滑动和滑后调整各阶段的变形特征。
1 区域概况
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目标滑坡为山西省某煤矿主井工业场地东南侧的一处古滑坡，其现今活动性对煤矿生产存在较大的安全隐患。研究区域位于山西省东南部重要含煤盆地内，该区为南北向大型复式向斜构造，地层主要由峰峰组、本溪组、太原组、山西组和第四系组成。滑坡体宽约550 m，长约230 m，整体变形范围较小。煤矿区域主要含煤层系为太原组和山西组，煤层平均厚度分别为5.25 m和3.18 m。煤矿于2019-06-22正式开工建设，开采深度已达456 m。
研究区域构造总体走向北北东，倾向北西，属于倾角5°~10°的单斜构造，伴有宽缓褶曲和小型断裂，局部地层倾角超过10°。研究区地势南高北低，海拔756.64~ 796.52 m，最大高差39.88 m，微地貌包括河流阶地、山麓斜坡和黄土残梁。坡面总体坡度10°~30°，呈台阶状分布(台阶高2~4 m)，植被茂密。区内地层主要由黄土状土、粉质黏土、含碎石粉质黏土及块石构成。黄土状土多呈硬塑状态，垂直节理发育，孔隙类型多样，土质较均匀。粉质黏土含少量砾石及砂岩碎块；含碎石粉质黏土碎石含量约10%~30%，粒径2~20 cm，局部夹杂砾石和砂岩孤石。块石主要为二叠系砂岩和泥岩，块体大小不均，大者数米，小者呈碎块状，多孔隙，部分由粉质黏土充填。夹层多为薄层风化泥岩，裂隙深度大，岩体破碎，局部呈散体土状，偶见薄层砂岩夹层。
自2020-09极端暴雨后，滑坡体趾部出现较强蠕动变形，挡土墙于2020-12锚索加固。本文通过高精度全站仪(测角误差0.5″，测距误差0.6 mm±0.1 ppm)监测滑坡体变形，采样时间间隔为10 d，2020-12起调整为1次/月，监测剖面平行于滑动方向，具体监测站分布见图 1，其中红色标记为测站位置，黑色垛墙线为挡土墙。监测点采用强制对中桩，地下部分埋深超过冻土层深度。
2 应变分析
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2.1 滑坡发生前坡体变形特征
采用基于小变形与有限变形条件的二维应变张量模型系统分析滑坡的时空变形特征。该模型以测点间基线长度和夹角变化为观测量，以基本应变张量{εx, εy, γxy}为待定参数，建立法方程组，并通过线性最小二乘法精确求解待定参数，以定量刻画滑坡体的复杂变形行为。模型的理论基础推导来源于文献[13]，本文将原始的平面直角坐标系修改为高斯平面直角坐标系，利用线性最小二乘法解算基本应变张量，并进一步计算面膨胀值和最大剪应变等关键的应变指标。其中，面膨胀值的正负变化可反映局部区域的扩张或压缩性质，而最大剪应变的极值分布代表滑坡变形在强度和方向上的差异性。
受局部滑动、垮塌、裂缝发育及施工破坏等因素的影响，各期观测均存在部分监测点缺失的现象，因此不同时期的应变场空间范围不完全一致。为便于对比变形强度随时间的变化趋势，本文采用统一色条绘制不同时期的应变场图。以三角形网络作为基本应变单元，分别在小变形和有限变形条件下建立应变模型，并通过计算2种模型所得应变张量参数的平均相对误差来评估模型精度。当单元相对误差大于0.01时，认为变形显著[14]。
研究区域属温带大陆性半干旱季风气候。据气象站观测，雨季主要集中在每年的7—9月，10月中旬至次年3月上旬为霜冻期，最大冻土深度80 cm。2020-09极端降雨与滑坡体及挡土墙的显著变形呈明显的时间对应关系，考虑到滑坡蠕动变形与降水通常具有滞后效应[15]，推测降雨为滑坡变形的重要诱发因素。
图 2显示，监测初期挡土墙水平位移与滑坡体前缘变形强度基本一致，均随时间衰减。2020-10—11，PC01测站附近挡土墙顶部出现宽1~2 cm、贯通长度超2 m的裂缝。面膨胀值显示，该裂缝区域局部压缩应变异常，最大应变率超过-125.8 μstrain。同期挡土墙变形强度显著高于滑坡体，表明挡土墙对滑坡的阻挡作用较弱。2020-12初完成锚索加固后，挡土墙位移强度显著衰减并趋于稳定。
面膨胀值分布表明，滑坡体前缘以压缩变形为主，后缘为微弱扩张，区域大致以各剖面02号测站连线为界。2020-10-17滑坡体前缘的PA和PB剖面间压缩应变率达-4.3 μstrain，中后部出现强膨胀及压缩变形极值。如PC02-PC03之间区域和PA04位置的强膨胀变形，以及PB03-PB04之间区域的强压缩变形。2020-12-03滑坡体前缘形成大范围压缩应变梯度带，与挡土墙加固时间相符。加固后，滑坡前缘滑动被抑制，中后部推挤导致物质堆积并加剧压缩。2021年后，滑坡及挡土墙位移趋于稳定，但2021-03-19滑坡体中后缘压缩应变强度首次高于前缘，PD03测站压缩应变率达-3.8 μstrain。
图 3显示，最大剪应变强度与面膨胀值的时变特征高度一致。2020-10滑坡活动最剧烈，挡土墙靠近PC01测站的局部区域出现剪应变极大值，达223.1 μstrain，主要集中在滑坡前缘和中部区域，表现为强烈的局部变形。滑坡体中后缘则形成明显的剪应变梯度带，高值区域反映了水平位移方向的显著发散。滑坡整体滑动主要分布于剪应变低值区，表明前缘滑动强烈，而后缘则受内部推挤引起的应变积累主导。2020-12挡土墙锚索加固完成后，滑坡体的相对变形显著减弱并趋于稳定。然而，加固作用使滑坡内部局部区域发生适应性调整，剪应变分布特征出现显著变化，如PD02-PD03、PC03和PB03-PB04区域的局部剪应变极大值揭示了滑坡体变形的不均匀性。这些区域的极值反映了挡土墙加固对滑坡变形控制的局限性，以及滑坡中后部的持续推挤作用对前缘变形的复杂影响。
2.2 滑坡滑动期间与滑后应变分析
2021-04-16—22滑坡体中后部发生局部失稳滑动。图 4所示的应变场为基于有限变形模型的计算结果。从图 4(a)可以看出，滑坡体整体受到前缘挡土墙较显著的抑制作用，以与滑动方向相反的回溯变形为主要特征。其中，PA和PB剖面各测站位移矢量存在明显的顺时针偏转。
面膨胀值(图 4(b))显示，滑坡体在该阶段以膨胀变形为主，局部极大值主要集中在中后缘，其中PB03-PB04之间区域面膨胀值达到最大的18.9 μstrain。最大剪应变分布(图 4(c))显示，滑坡后缘的差异变形强度高于前缘，应变极值出现在PC03和PC04之间区域，达到145.2 μstrain。值得注意的是，PB03与PB04之间区域既是最大剪应变的强-弱突变区域，又是面膨胀值的极值区域，表明该区域存在剧烈的局部变形。
图 5第1行为滑后调整阶段的面膨胀值分布，第2行为最大剪应变率分布。面膨胀值强度随时间衰减迅速，2021-07滑坡体内部相对变形已十分微弱。最大剪应变率变化范围虽然随时间逐步缩小，但极大值几乎未减弱，表明滑坡体内部仍然存在显著的差异变形。2021-05-28，PC02既是滑坡体前缘膨胀和后缘压缩的应变节点，又是最大剪应变的极值区，达60.1 μstrain。PB03-PB04始终是整个滑坡体的异常变形节点，具有局部强应变集中特征。挡土墙在滑动失稳阶段的最大剪应变高值区主要集中在中段，而滑后阶段(2021-05-28—06-23)剪应变极大值广泛分布在整个挡土墙之上，表明该阶段挡土墙受到滑坡物质的冲击作用较为分散。
3 讨论
收起
3.1 应变张量参数的最小二乘求解
根据文献[13-14]，应变可定义为变形点位移的函数，本文变形监测结果恰为离散点位上变形信息的表达。因此解算本文所推导的应变模型时，最好以实际观测站为节点进行边连式多边形网络单元剖分，以各单元顶点的实测变形信息建立观测值法方程，并采用最小二乘法求解各单元的基本应变张量参数{εx, εy, γxy}。通常可以利用3个测站组成三角形单元，也可选取四边形、五边形等多边形图形单元。
解算应变模型时，法方程中的观测值向量为相邻两期观测到的实测点位置信息的相对变化量，如基线长度和基线夹角[16]，由连续两期的实际观测值差分得到。因此，基于图形单元计算得到的应变张量参数在本质上是对应区域范围在观测周期内的平均应变值。采用图形单元法计算应变场时，应划分尽可能小的图形单元，以使应变计算结果更加符合应变场的空间连续分布特征。显然，三角形单元是能支撑最小二乘求参的最基础应变单元，其占用的离散实测点位数量最少，所覆盖区域的平均面积最小，可以最大程度地提高所计算应变场的空间分辨率。
本文以离散观测站为顶点，在研究区域划分Delaunay三角形网络。在连续两期观测中，三角形单元的边长变化表示实测站之间的距离变化，内角变化表示对应基线之间的夹角变化，由此建立基本观测值方程。模型解算的关键在于构建合理的权阵，测站数据的精度和空间尺度是确定各测站对应变单元参数影响的重要依据[17]。
目前，常用的加权方法以图形单元的形心为应变计算参考点，测站与形心距离的倒数或倒数函数作为权重。该方法假设测站与参考点距离越远，变形相关性越弱。但此方法对每个应变单元内应变值的统一性考虑不足。因此，本文采用Voronoi多边形进行划分，利用Delaunay三角形格网切割Voronoi单元，将各实测点的局部面积作为权重。这种基于局部面积的加权方法更能反映应变单元内变形的空间分布特征。
3.2 应变参数的可靠性
受经费和实验场地限制，本文未能在研究区域安装同步应变仪进行对比观测，因此采用Monte Carlo方法评估应变计算模型的可靠性。Monte Carlo方法基于概率模型，通过随机样本的重复计算模拟误差分布，无需复杂的误差传播公式，能够在缺少实测应变数据的情况下合理评估应变张量参数的精度与模型稳定性。
以PB02测站为例，选取2020-10-28(滑动前)、2021-04-22(滑动期间)和2021-07-23(滑动后)3个时段的位移场数据为代表，利用符合标准正态分布的随机噪声模拟观测误差，通过Monte Carlo算法执行50 000次循环计算，生成面膨胀应变值与最大剪应变值样本。统计分析表明，在不同变形阶段，PB02测站的特征应变参数分布均表现出较高的集中性，标准差处于合理范围内(图 6、7)，验证了应变模型计算结果的稳定性与可靠性。
3.3 监测频率与数据时效性对失稳前兆捕捉的影响
1) 监测频率和数据时效性的限制。在滑坡监测过程中，监测频率和数据时效性对失稳前兆的捕捉具有重要影响。本文采用10 d或1次/月的监测频率，而滑坡失稳前兆往往在较短时间内(如几小时或几天)快速发展。因此，现有的监测频率无法满足对滑坡局部失稳前兆的精细捕捉。这种频率限制使得图 2和图 3中的位移与应变分布无法直接反映2021-04-16—22滑坡体局部失稳的前兆信息。
2) 应变和位移敏感性的局限性。滑坡失稳前兆可能表现为应变的局部集中或极值的急剧变化，而非大范围的位移累积。尽管本文通过应变分析获取了滑坡体变形特征，但图 2和图 3主要反映了滑坡整体的位移变化趋势，未能充分展示应变在失稳前兆阶段的微小变化。因此，位移监测结果在整体趋势上较为平稳，缺乏对局部快速应变变化的敏感性，导致局部失稳的前兆难以显现。
3) 数据连续性的局限性。滑坡体的局部失稳通常在较短时间内发生并演化，而本研究监测数据的时间间隔较大，缺乏连续性。在此条件下，图 2和图 3中数据显示了较长时间间隔的平均变形分布，无法展示2021-04失稳前的精细变化。未来若缩短数据采集时间间隔或引入更高频率的准实时监测技术，可能有助于更敏锐地捕捉滑坡的局部失稳前兆。
3.4 应变极大值的局部集中
挡土墙最显著的变形特征为裂缝位置应变极值梯度带。图 8(a)为挡土墙顶面位于PC01测站东北侧区域出现的一条约2 cm×2 m的裂缝。该位置是面膨胀值和最大剪应变极值集中区域，特别是在变形监测初期坡体前缘强蠕变变形阶段。应变极值区通常代表着变形最剧烈的部位，裂缝的存在显著加剧了变形体的局部变形，并形成应变极值集中现象。
PB03与PB04之间区域发育有滑坡体表面最显著的一条裂缝(图 8(b))。对比PB03-PB04与坡体其余部位的面膨胀值和最大剪应变值(图 9)可知，2020年底临近滑坡发生时，该位置的面膨胀值具有极大值特征，且存在变形极值和变形属性的同步变化。2020-11-19—12-03应变极值变化量超过20 μstrain，最大剪应变则长期高于坡体平均水平。
Guerriero等[18]研究发现，滑坡失稳通常从局部破坏开始。本文应变分析结果表明，应变极值的局部集中现象与裂缝活动密切相关，是滑坡非稳定演化的重要指标。在斜坡后缘发生局部滑动前，坡体整体处于准静止状态，图 2、3中的位移矢量趋近于0，但PB03与PB04之间裂缝位置的应变强度仍显著高于整个滑坡体。面膨胀值在临近滑坡发生时变形属性的频繁变化表明，即使绝对位移不显著，局部裂缝的发育活动仍在持续，滑坡仍存在潜在失稳风险。
4 结语
收起
1) 滑坡变形的空间分布特征：滑坡体表现出显著的前缘压缩和后缘扩张特征，压缩-扩张区域具有明显的分界，前缘压缩区的应变强度高于后缘。滑坡内部应变极值沿裂缝分布，形成高应变梯度带。
2) 滑坡变形的时序变化规律：随着时间推移，滑坡前缘的压缩变形显著衰减，而后缘的应变强度则在滑后调整阶段呈现持久性。这表明滑坡在失稳后的应变恢复存在较强的区域差异。
3) 应变分析在滑坡监测中的作用：应变率作为定量描述滑坡变形强度的有效指标，可揭示滑坡内部的局部变形特征和裂缝活动趋势，为滑坡变形机理研究和风险预警提供可靠依据。
综上所述，本研究的应变分析方法为滑坡体变形的定量化描述提供了新的视角。通过对不同演化阶段的应变特征进行分析，可更好地理解滑坡活动的动态特征，为类似滑坡的监测与预警提供重要支持。

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doi: 10.14075/j.jgg.2024.10.498
  • 接收时间：2024-10-31
  • 首发时间：2026-10-29
  • 出版时间：2025-11-15
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  • 收稿日期：2024-10-31
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    1 陕西省一八五煤田地质有限公司, 陕西省榆林市人民西路283号, 719000
    2 西安科技大学测绘科学与技术学院, 西安市雁塔中路58号, 710054

通讯作者:

吴啸龙, 博士, 讲师, 主要研究方向为高危变形体动态变形监测与预警, E-mail:

WU Xiaolong, PhD, lecturer, majors in dynamic deformation monitoring and early warning of high-risk deformation bodies, E-mail:

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